Nice Exponent Math Simplification | Find the Value of X
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Another equivalent approach: 3(9ˣ) = 999 9ˣ = 333 log₉9ˣ = log₉333 x(log₉9) = log₉(9•37) x = log₉9 + log₉37 x = 1 + log₉37
@michaelandcarmenmaguire11085 ай бұрын
Calculators don't have log3 or log9 buttons, so a better solution is: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
@RobbieHatley4 ай бұрын
@@RobbieHatley Interesting. Why assume that we have a traditional scientific calculator on hand, and why assume that that's the tool we have to use? With the right app on a computer or a smartphone, you can absolutely ask for log[9]333, and get there directly
@douglaswolfen78204 ай бұрын
@@RobbieHatleyfor that matter, why assume that we're looking for a decimal approximation? Your answer is only correct to 5 significant figures, but the answer in the other comment (just like the answer in the video) is _exactly_ correct The objective isn't always to calculate the precise value in decimal notation. Sometimes the objective is to simplify the number down as far as you can, like they did in the video
@douglaswolfen78204 ай бұрын
@@douglaswolfen7820 : The reason "decimal approximation" is useful is that that is the system humans use for engineering. "Exactly Correct" is an abstract concept useful only for getting marks on school tests; to actually *_use_* an abstract "number" such as "log[9](333)" one must convert it to "about 2.64339956411" (use however few or many digits the application calls for). And most calculators (and calculator apps) do not have log[3], log[9], or log[n], only log[e] and/or log[10]. If you can find such apps, good for you. But all you've achieved with wasting 5 hours searching for such apps is that you've saved the additional 5 seconds of your time it takes to do log[b](x) = ln(x)/ln(b). 🙄
@RobbieHatley4 ай бұрын
@@RobbieHatley It’s true that many calculators only have log[10] and ln. But one can easily convert to any base by using the change of base formula, as demonstrated in your solution using ln. Log[10] could also have been used, achieving the same result. I agree with others that a numeric solution is only an approximation, but I also like doing the calculation to validate the solution.
@davidpoulin69614 ай бұрын
In the third step you can do: x = log(333)/log(9) and avoid the rest.
@Bolasiebendrei6 ай бұрын
@@vladimir.univer6123 No, log(333) / log(9) is much simpler than all the extra extraction that gets nowhere. Nowhere is log9(value) better !
@johncampbell78685 ай бұрын
How are you gonna do that without a calculator though?
@MathGPT5 ай бұрын
Log(333) and log(9) can be simplified, so it’s not entirely a waste. All the factors of three could have been dealt with simultaneously though. log_3(37) is not simplified though. Leaving the log in the natural base is better than any arbitrary base
@brandonhicks75495 ай бұрын
Good comment: for x=log(333)/log(9) you can use ANY log base. Yes, for me it's the best answer. Better than? x=1+log(37)/log(9) or 0.5x(1+log(111)/log(3)); any log base
@tagben855 ай бұрын
Yes I changed the sum into 3×9^x and than division with 3. Later log(9)/log(333) . it's about 2.64 .
@SmaugAltair5 ай бұрын
Hmmm... I'd hardly consider it simplified if the final expression has a base 3 logarithm
@zameb93746 ай бұрын
Should have gone for base 10
@raviprakashvs12135 ай бұрын
I can simplify it much more. Log(base:3) ^37 equals to 3.3(approx) , so x= 2.7(approx) Just have to see how many times you can multiply the base number (I.e. 3) with itself until you reach a smaller number closest to root (I.e. 37) . So, 3 x 3x 3 = 27 which is a smaller number closest to 37. So the number of times the base number was able to be multiplied by itself is 3. Then the same base (I.e. 3) is to be divided with the remaining part of root which is (37-27)= 10. So 3/10 = 0.3 Now you add that '3' ( which you obtained by seeing how many times the base number was multiplied with itself to reach a value closest to root) with 0.3 I.e. 3+0.3= 3.3 (value of log 37 base 3) Now the remaining part can be calculated easily
@DbCo0pEr5 ай бұрын
😁👏👏😂😂😂
@kalyannatarajan16955 ай бұрын
算這個要幹嘛
@user-nu5oj5xm5k4 ай бұрын
В России цифру 7 пишут в записях с черточкой - чтобы не спутать с 1… посмотрите русскоязычные ролики про математику пожалуйста
@tradetranscom4 ай бұрын
The 20 minute answer to the 5 second question.
@ronaldkearns60575 ай бұрын
Yes agree
@leoku004 ай бұрын
Exactly 😅
@pierluigibelcaro99502 ай бұрын
This was really painful to watch as a math professor, yet oddly riveting I couldn’t look away
@MathGPT5 ай бұрын
lol same here
@paulandaloro85144 ай бұрын
You should pass unnessesary part. So much detail make watchers bored. For example, like 2/2=1, you don't need to explain it over and over. A watcher who had already understood about 'log', He will be very bored seeing you explain why 2/2 becomes 1.
@JohnCrawlyks4 ай бұрын
Отличное видео,чтобы уснуть,можно непослушным детям показывать и самому смотреть).
@user-ey5cs6kf2t4 ай бұрын
The hardest part is knowing what this is good for.
@jcasey83355 ай бұрын
Exactly.
@MrWaalkman5 ай бұрын
If you work in any technical field like electronics are mechanical design you'll know.
@raviprakashvs12135 ай бұрын
@@raviprakashvs1213 Like say, as a retired Controls Engineer from GM? Care to enlighten me? I must have missed its significance at some point in the last 35 years. :)
@MrWaalkman5 ай бұрын
@@MrWaalkman what algebra or exponents are good for?.. jeez if you hadn't by now, I don't think anybody could it.
@raviprakashvs12135 ай бұрын
@@raviprakashvs1213 We just never used them. But if you were a Controls guys you would have known that.
@MrWaalkman5 ай бұрын
Video was over twice as long as it needed to be. Even playing at 2x speed this felt extremely slow (and I haven't done this sort of math in over 30 years) because you write so slowly and add all sorts of extraneous gestures. Time compression of about 2.5~3 would be appropriate before adding music soundtrack.
@akulkis5 ай бұрын
That's not a simplification, it is a complification 😢
@TommyRaines5 ай бұрын
Yes. If he'd calculated this the easy way, the solution would have looked like this: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
@RobbieHatley4 ай бұрын
You could as well take the log early on, if the shown way in the end leads to a log anyway.
@viennabartsimpson16605 ай бұрын
Why is it so satisfying to draw the box around the answer?
@SevenIsaCannibal75 ай бұрын
Why so difficult? 3^2x = 333 is equivalent to 2x = log3(333) by logarithm definition itself. Then spread out 333 to 9*37, get 2x = log3(9) + log3(37), x = (2 + log3(37))/2 and finally x = 1 + log3(37)/2 Of course, it's useful to go the long way sometimes, but I've thought I do something wrong first. )))
@user-qq5kv6nd6h5 ай бұрын
Well, I got as far as "9^x has to be 333" and knowing that 9² is 81 and 9³ is 891 I just said "then x must be a little more than 2,5 = good enough for me" 😄 fast approx solution, I did calculate logarithms in school but never got attached to them, similar to integrals. I even had to do those in my oral exam, but never really got the hang of them, so naturally forgot all about their usage. They must have been easy, though, I did everything right and they just had one clarification question.
@cailleanmccain4 ай бұрын
I mean does it need to be that long 😂😂😂. You could have solve it in less than 5 lines 😂😂. But thanks for the good old math, it brings me back to my college years.
@84Iboga5 ай бұрын
....2.6433996 is as near as you will get in simple figures.😊
@garydavis26886 ай бұрын
2.643399564
@IPWCsInTheory5 ай бұрын
@@IPWCsInTheory Exactly. Good enough for me. So the poster here would still have to face a scientific calculator, or a log table. The long solution presented is therefore a futile exercise.
@OldPannonian3 ай бұрын
I find logs hard to follow. We got the answer for x but it is meaningless to me until I calculate a decimal equivalent afterwards. The abstract nature of calculus gives me the same fits. Geometry, trigonometry, and simple algrebra are not too bad though.
@ryanab015 ай бұрын
You dont need to calculate logs. There are tables which you can refer which makes it a lot easier.
@raviprakashvs12135 ай бұрын
@raviprakashvs1213 yes, it's been a long time since I've used them, but it's starting to return to me. Also, if I think about logs being inverse to exponents, then I can begin to visualize that, too.
@ryanab015 ай бұрын
Can't you just divide 999 by 3 and find base 9 log of 333?
@mr.pumpkinn5 ай бұрын
Yup! But then the video would be a lot shorter and they'd rack up less watch time
@douglaswolfen78204 ай бұрын
Excelente explicación, paso a paso perfectamente explicado. Gracias
@juancarlosarizabarajas53464 ай бұрын
Más didáctico no podia ser ! Bravo!
@geminisloha58785 ай бұрын
Everything calculated correctly... great... What annoys me is the background music. It would also be nice if you wrote that X=2.6434. It's a thumbs up from me.
@ronaldnoll32475 ай бұрын
Why didn't you take log with base 3? I think this is the best simplification because we now don't want a approximated value.
@shelfspring4 ай бұрын
Inefficient.
@pooyakoohbanani91445 ай бұрын
Very
@mompatimase1672 ай бұрын
or simpler: X = 1 + log9( 37 ).
@21065226 ай бұрын
the very case when the result is longer and more incomprehensible than the original task
@ilyacheker33465 ай бұрын
Knowing if your computer program that solves maths for users works properly
@Ozymandias835 ай бұрын
If done right, this video would only have been about about 15 seconds long: 3(9^x) = 999 9^x = 333 ln(9^x) = ln(333) x * ln(9) = ln(333) x = ln(333)/ln(9) ≅ 2.6434
@RobbieHatley4 ай бұрын
Great work man. And perfect speed. People dont get the fact that everyone is different. Mathematically half the people are below median intelligence, so that might be the reason. Subscribed.
@fminc5 ай бұрын
Hey what device do you use for filming?
@erdincyerdelen97322 ай бұрын
I found all three. They’re right next to the 9’s.
@Mythicalniceguy5 ай бұрын
A lot of unnecessary steps
@bertberw86535 ай бұрын
I agree very slow
@dinomijatovic39212 ай бұрын
Wow, I’m not really sure I see the point of that exercise. The reduction to 9^x=333 was so obvious, I thought it would be your starting point; then 333/9 = 37 (x is not a whole number so 2). I’d iterated that out to roughly 2.6433997 (somehow kind of thought you’d lead me to a round number) before you churned out a log equation.
@kevinoboyle89395 ай бұрын
2,6434 more correct :))
@borisoff4095 ай бұрын
@@borisoff409 Maybe in Europe, but here in the U.S. you’re off by several orders of magnitude!
@kevinoboyle89395 ай бұрын
For teaching purpose is ok，could start by 3x9^2=243, 3x9^3=2187, so x should btw 2 and 3，and 3x9^2.5=3x9^2x9^(1/2)=729, so move further to x is btw 2.5 and 3 ，without cal and table the answer is 2.5
@user-gq2oj2nk4h3 ай бұрын
2,6434
@user-mj1wb3fr7d3 ай бұрын
Assume x = 1 n then drop + signs... Problem solved!!!😁😂😊😄🤩
@prashantpandya15085 ай бұрын
I thought the answer should be integer.
@user-rj4db3ve4w5 ай бұрын
What is the point of just simplicifaction, if the answer still sits with a log expression. Ultimately, one would wish to arrive at a pure numerical value. Therefore, you still need a calculator or a log table. In that case, it would only take 4 lines to arrive at the final value. (Signed: an old non-scientific, non-math guy, riddled with arthritis, but still with a working brain.)
@OldPannonian3 ай бұрын
Shorter: 3*9^x = 999 9^x = 333= 9*37 therefore 9^(x-1) = 37 I get x-1 = log 37÷ log 9 or X= 1 + log37/ ( 2* log 3)
@herbertklumpp29697 ай бұрын
.... = 1 + LOG (base 3) [ SQRT(37) ] ...
@jan-willemreens90106 ай бұрын
True. And if the base = 9, X = 1 + log9(37) / log9(9) = 1 + log9(37).
@21065226 ай бұрын
Great Math Solution!!!
@ollilui4 ай бұрын
Не получилось решить? Ну, может тогда на калькуояторе...
@mmxxivSerg6 ай бұрын
If I calculated this slowly, I would still be in 5th grade.
@shaanmuneeb63395 ай бұрын
Gosto muito dessas explicações. Porém, nesse caso específico, o resultado encontrado não ajuda muito sem uma calculadora ou tábua de logaritmos. Mas, se fosse pra usar um ou outro, poderia ter resolvido sem fazer nada disso. Muito obrigado
@fernandocarvalho21682 ай бұрын
I had to downvote. the title suggests an interesting problem that might have an elegant solution, maybe even no calculator required. After three lines of slightly slick transformation, it became a recap of logarithmic laws in slow motion landing at a calculator solution.
@bernhardmartl46755 ай бұрын
You expect me, the reader, to know logs & logs to base 3, but you take me thru those basic school processes of simplification? LoL 😂. It could be done in ¼ the steps & ¼ the time.
@raghu453 ай бұрын
Merci. Très bien expliqué
@abdellatifouladaarab93523 ай бұрын
This was the most agonizing 6 centuries-sorry I meant MILLENNIA of my life. The most efficient approach is the simplest, most convenient and fastest: 9^x + 9^x + 9^x = 999 9^x • 3 = 999 9^x = 333 x = log_9(333). This literally only took 3 steps to calculate other than just copying the problem down. Unbelievable. Go formulate 2 brain cells to rub together.
@VodkaTheAntiAlcoholic5 ай бұрын
Basically writing the solution to one equation in terms of the solution to another, because log_3 37 is just the solution to 3^y = 37.
@stephenpenrice12305 ай бұрын
At this point just divide it all by 2 right away, or simplify it even more.
@OnFight19973 ай бұрын
A simple question. Brought me to my school years
@polyglot90094 ай бұрын
I solved it to 4 significant figures just by punching in 9 to the power of various "X's" in an old business HP RPN calculator to get 333 in less than 1/4 the time you took to write all of that - without providing an actual numerical answer. I now forget what I had but it was something like 2.6433 and I didn't go any further. I believe I could have solved it directly to more significant digits in less time if I had my engineering scientific HP calculator on my desk (its in my briefcase).
@perryallan35245 ай бұрын
yep, did the same thing. Took about 1 minute. Got it to 4 decimals.
@cosmicinsane5165 ай бұрын
Да, всё правильно. Если в ответе остаются знаки математических операций - такой ответ ничего не стоит
@Gravitorrr5 ай бұрын
It easy very easy for a experienced guy in aproach The correct logarithm of that..,..The bases are equal..,
@user-wf1es2lp9s5 ай бұрын
@@user-wf1es2lp9s That would have required me to have my engineering calculator available as only it has log functions on it. As an engineer I look for the fastest way to solve a problem. Not necessarily the most elegant way. As a result math problems are often solved more quickly with simple calculation attempt methods as I used above. Now real engineering issues can take weeks of work to come up with a good approach and a likely range of solutions; then you pick the best choice (and document why you picked that one - as you don't always pick right).
@perryallan35245 ай бұрын
с начала было более приятным когда не знали значение х, чем когда знали значение что ровна какому то не знаю чего😁😁😁
@narek83063 ай бұрын
You can solve that equation in 2 steps, divide both sides by 9 to give 3x then divide 111 by 3 to give x = 37!!!
@scottbishop78993 ай бұрын
Nice
@shashikantvairat80737 ай бұрын
А в цифрах есть ответы? Какю цифру вместо "x" поставить нужно?
@DOCTORHEAVY2312 ай бұрын
X = 1 + ln(37)/2 ln(3)
@dhy53426 ай бұрын
True. But a simpler equivalent equation is: x = ln(333)/ln(9)
@RobbieHatley4 ай бұрын
I would say: 3(9^x) = 999 9^x = 333 e^(ln9)x = e^ln333 (ln9)x = ln333 x = ln333/ln9 = 2.6433
@pierluigibelcaro99502 ай бұрын
Можно было сразу сократить 3^2x=333 => 3^2x=3^2×37 => 3^x=37
@modikv63065 ай бұрын
I think the simplest answer to this Problem is x=log333 (base 9)
Where did you get log ( 3 .37) where dud yiu get this 37 from??😮
@hansenriquerach-mendoza35156 ай бұрын
111/3= 37
@hendrikpingel48476 ай бұрын
333/9 = 37.
@21065226 ай бұрын
К чему такие длиные выводы, если можно сразу находить логарифм от 37 по основанию 9 +1 или есть таблицы логарифмов с онованием 3. Всё равно надо брать таблицу натуральных логарифмов и ln37/ln9+1=приблизительно 2,64
@user-lh4vx1ny4j4 ай бұрын
Is there a point not stopping at x=log333/log9 ?
@bizmyurt85823 ай бұрын
How do calculate the log of base 3 of a number?
@pb19636 ай бұрын
Whit a log table. Or with a calculator.
@iorguemaxwell6 ай бұрын
log(x) / log(3)
@Arnie101016 ай бұрын
Basically you don't.
@bztube8885 ай бұрын
Calculators and computers only provide bases e and 10, so you have to convert to one of those. The standard way is to convert everything to base e, using this formula: log[b](a) = log[e](a)/log[e](b). Calculators usually call log[e] "ln", but many programming languages call it just "log". More specifically, the problem in this video should have been done like this: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
@RobbieHatley4 ай бұрын
I don't think it was clear. I meant, use the base change property: log of "n" in base "b" = log of "n" in base 10, divided by log of 3 in base 10. Or, base "e" if you prefer.
@iorguemaxwell4 ай бұрын
2,6434 would be good enought. Aproximation seems way simplier anyway, but good thought process thou.
@celsojr4 ай бұрын
And the additional step of showing the actual answer is not included because...?
@hatchermoney3 ай бұрын
One equation in one unknown .. 10 secs at most
@tobybarker68085 ай бұрын
Took me 15 seconds. But then, I'm rusty at math. As for the guy in the video, he's obviously much _more_ rusty, as he never does find the correct answer: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
@RobbieHatley4 ай бұрын
How can log(111) be equivalent with log (3.37) Please explain it to me!
@user-yv1xc6dr2z3 ай бұрын
very good. thanks
@user-lk5em7ug4b4 ай бұрын
Basta applicare la definizione di logaritmo dall'esponenziale e' x uguale a log in base 9 di 333.
@MAUROMINERVINI-hh9pc2 ай бұрын
Ответ еще страшнее выглядит чем дано
@MrTuflya5 ай бұрын
En la última parte simlifica sin hacer facror común, me parece que esta mal
@enriqueestebanSchott5 ай бұрын
So the short answer is you don't know the answer?
@jeffmcrae53364 күн бұрын
Sir can't we solve it without using logarithm?
@Chawlas573 ай бұрын
Lord help us.
@michaeltelemachus51125 ай бұрын
Did it my head within a couple of seconds
@recruitmentanarchist4 ай бұрын
Why do you write 1+1+1=3
@2d07hochunhei35 ай бұрын
See logarithms ARE useful after all 3(9^x) = 999 9^x = 333 x = log(333)/log(9) ~2.6434
@dackhornbold17285 ай бұрын
Aw, but then his video would only have been 15 seconds long and where's the ad revenue in that? 😉
@RobbieHatley4 ай бұрын
Btw some ppl like me only see videos while muting the audios, thus every step helps 🤷♀️
@tasnuvarahman91155 ай бұрын
Самое сложное было понять, что это 9, а не q
@user-qu7ge6hf6i3 ай бұрын
Why does he write the "7" without the stick?
@unapersona83573 ай бұрын
Divide all by 9 and you arrive to 2(x-1)log3 = log 37
I’m gonna need a number. Does that equal a number?
@MichaelStanwyck5 ай бұрын
If you have to use a calculator anyway, why not just stop at log9(333)? How is 1+0.5*log3(37) a better or simpler answer in anyway?
@yikaiye92415 ай бұрын
Calculators don't have log[9] buttons, so a more practical solution is as follows: 3(9^x) = 999 9^x = 333 ln(9^x) = ln(333) x * ln(9) = ln(333) x = ln(333)/ln(9) ≅ 2.6434
@RobbieHatley4 ай бұрын
@@RobbieHatleywho's using a calculator? Surely it would be be an app or a computer program these days? And if a modern app doesn't have a "log base x of y" function, then it really ought to
@douglaswolfen78204 ай бұрын
@@douglaswolfen7820 : Re "Who's using a calculator": You can use a slide rule if you like, it's all the same to me (though not as easy). Re "ought to": If wishes were fishes we'd all own chains of lucrative seafood restaurants. 🙄 The fact remains, most calculators, apps, log tables, and computer programming languages don't have log[3], log[9], or log[n], just log[e] ("ln") and/or log[10], so it's advantageous to learn the base change formula: log[b](x) = ln(x)/ln(b), or just do everything using natural log from the start: 3(9^x)=999 9^x=333 ln(9^x)=ln(333) x*ln(9)=ln(333) x = ln(333)/ln(9) ≅ 2.64339956411...
@RobbieHatley4 ай бұрын
@@douglaswolfen7820 : Re "ought to": woulda shoulda coulda. That's not the world we live in. In the world we live in, most (physical) calculators, calculator apps, web math sites and calculators, and computer programming languages, have logs to base e and 10 only. However, that's not a problem, because log[b](a) = ln(a)/ln(b), so only natural (base e) logarithms are needed. If this principle is applied to the problem at hand, it becomes easy to find both the exact answer and a decimal approximation, in about 15 seconds: 3(9^x) = 999 9^x = 333 x = log[9](333) x = ln(333)/ln(9) (exact answer) x ≅ 2.6434 (decimal approximation)
@RobbieHatley4 ай бұрын
@@RobbieHatley huh. I just checked the one on my phone and you're right. I'm disappointed though
@douglaswolfen78204 ай бұрын
Right answer is X=2.6434. We all are calculat and find the answer is 2.6434 only.
@parmararun14752 ай бұрын
My wife wants to know, what is this math used for?
@Skiskiski5 ай бұрын
Science and engineering usually
@douglaswolfen78204 ай бұрын
Found it... Its on top of the 9
@totallynotthefeds364 ай бұрын
Can u solve without logorithm?
@Mochi_kitty9235 ай бұрын
No. It is an inherent part of solving for a variable exponent as logarithms are the inverse of exponentiation. (a common misconception is that taking the root of a value is the inverse of exponentiation, but actually the radical is just a fancy way to denote that the root value is the denominator of the exponent). So, to solve a^x=b, you can only isolate x to one side by taking the logarithm of both sides, getting x = log_a (b) after a bit of simplifying.
@TSPxEclipse5 ай бұрын
This problem involves logarithms pretty much by definition. You've got a base (9), you're raising it to an exponent (x) and you've got the result (333). You know the base, you know the result, and you're trying to find out what value the exponent has. That's what a logarithm _is_
@douglaswolfen78204 ай бұрын
It's right there 4 times shown on the screen.
@sofexpert4 ай бұрын
The answer is more difficult.
@VitorJKhan5 ай бұрын
4:25 How did log111 convert into log(3.37)? Hooow?
@AliKhan-jt6zj5 ай бұрын
log(111)=log(3×37)=log(3.37)
@Adrenalinclip5 ай бұрын
@@Adrenalinclip you mean 3*37=3.37? 🤷♂️
@AliKhan-jt6zj5 ай бұрын
Shouldn't there be an actual member at the end of all of this? Edit: number not member
@waynemiller60705 ай бұрын
From a certain point of view, the answer given _is_ a number. It's just a number written in a weird way And yes, sometimes you need to write it out as a traditional decimal number, like "2.6394747” or something. But there's a problem with that: the real number would be infinitely wrong, so you can only write an approximation, not the actual number. Sometimes it's better to just write down the calculation and stop there
@douglaswolfen78204 ай бұрын
How about x = log111/log9.
@VinceLongo-pz6ze5 ай бұрын
What’s wrong with 333 divided by 9 to give x ?
@sobeit19276 ай бұрын
I don’t even understand the question ! Lol😂
@sobeit19276 ай бұрын
Because it is incorrect. It is the 9th root off 333. Easier to do on a calculator than log3.
@gwflew6 ай бұрын
Everything.
@bztube8885 ай бұрын
That would yield 37, which is the wrong answer. (The actual value is about 2.6434) The correct solution is as follows: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
@RobbieHatley4 ай бұрын
Фундаментальная ошибка их образования во всей красе. Ответ находится в два действия. А если нужно число, то его посчитает любой онлайн калькулятор. То есть сами себя загнали в глупые рамки и от математики не остается и следа.
@user-wi8iq3hn3k3 ай бұрын
you can also put a ring through your nose
@bayantse30003 ай бұрын
So log base 3(999) = 2π, or log base 9(999) = π :)
@sergten5 ай бұрын
Close! Within 1 part per thousand. Not exact, though. log[9](999) ≅ 3.1434 whereas π ≅ 3.1416
Another equivalent approach: 3(9ˣ) = 999 9ˣ = 333 log₉9ˣ = log₉333 x(log₉9) = log₉(9•37) x = log₉9 + log₉37 x = 1 + log₉37
Calculators don't have log3 or log9 buttons, so a better solution is: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
@@RobbieHatley Interesting. Why assume that we have a traditional scientific calculator on hand, and why assume that that's the tool we have to use? With the right app on a computer or a smartphone, you can absolutely ask for log[9]333, and get there directly
@@RobbieHatleyfor that matter, why assume that we're looking for a decimal approximation? Your answer is only correct to 5 significant figures, but the answer in the other comment (just like the answer in the video) is _exactly_ correct The objective isn't always to calculate the precise value in decimal notation. Sometimes the objective is to simplify the number down as far as you can, like they did in the video
@@douglaswolfen7820 : The reason "decimal approximation" is useful is that that is the system humans use for engineering. "Exactly Correct" is an abstract concept useful only for getting marks on school tests; to actually *_use_* an abstract "number" such as "log[9](333)" one must convert it to "about 2.64339956411" (use however few or many digits the application calls for). And most calculators (and calculator apps) do not have log[3], log[9], or log[n], only log[e] and/or log[10]. If you can find such apps, good for you. But all you've achieved with wasting 5 hours searching for such apps is that you've saved the additional 5 seconds of your time it takes to do log[b](x) = ln(x)/ln(b). 🙄
@@RobbieHatley It’s true that many calculators only have log[10] and ln. But one can easily convert to any base by using the change of base formula, as demonstrated in your solution using ln. Log[10] could also have been used, achieving the same result. I agree with others that a numeric solution is only an approximation, but I also like doing the calculation to validate the solution.
In the third step you can do: x = log(333)/log(9) and avoid the rest.
@@vladimir.univer6123 No, log(333) / log(9) is much simpler than all the extra extraction that gets nowhere. Nowhere is log9(value) better !
How are you gonna do that without a calculator though?
Log(333) and log(9) can be simplified, so it’s not entirely a waste. All the factors of three could have been dealt with simultaneously though. log_3(37) is not simplified though. Leaving the log in the natural base is better than any arbitrary base
Good comment: for x=log(333)/log(9) you can use ANY log base. Yes, for me it's the best answer. Better than? x=1+log(37)/log(9) or 0.5x(1+log(111)/log(3)); any log base
Yes I changed the sum into 3×9^x and than division with 3. Later log(9)/log(333) . it's about 2.64 .
Hmmm... I'd hardly consider it simplified if the final expression has a base 3 logarithm
Should have gone for base 10
I can simplify it much more. Log(base:3) ^37 equals to 3.3(approx) , so x= 2.7(approx) Just have to see how many times you can multiply the base number (I.e. 3) with itself until you reach a smaller number closest to root (I.e. 37) . So, 3 x 3x 3 = 27 which is a smaller number closest to 37. So the number of times the base number was able to be multiplied by itself is 3. Then the same base (I.e. 3) is to be divided with the remaining part of root which is (37-27)= 10. So 3/10 = 0.3 Now you add that '3' ( which you obtained by seeing how many times the base number was multiplied with itself to reach a value closest to root) with 0.3 I.e. 3+0.3= 3.3 (value of log 37 base 3) Now the remaining part can be calculated easily
😁👏👏😂😂😂
算這個要幹嘛
В России цифру 7 пишут в записях с черточкой - чтобы не спутать с 1… посмотрите русскоязычные ролики про математику пожалуйста
The 20 minute answer to the 5 second question.
Yes agree
Exactly 😅
This was really painful to watch as a math professor, yet oddly riveting I couldn’t look away
lol same here
You should pass unnessesary part. So much detail make watchers bored. For example, like 2/2=1, you don't need to explain it over and over. A watcher who had already understood about 'log', He will be very bored seeing you explain why 2/2 becomes 1.
Отличное видео,чтобы уснуть,можно непослушным детям показывать и самому смотреть).
The hardest part is knowing what this is good for.
Exactly.
If you work in any technical field like electronics are mechanical design you'll know.
@@raviprakashvs1213 Like say, as a retired Controls Engineer from GM? Care to enlighten me? I must have missed its significance at some point in the last 35 years. :)
@@MrWaalkman what algebra or exponents are good for?.. jeez if you hadn't by now, I don't think anybody could it.
@@raviprakashvs1213 We just never used them. But if you were a Controls guys you would have known that.
Video was over twice as long as it needed to be. Even playing at 2x speed this felt extremely slow (and I haven't done this sort of math in over 30 years) because you write so slowly and add all sorts of extraneous gestures. Time compression of about 2.5~3 would be appropriate before adding music soundtrack.
That's not a simplification, it is a complification 😢
Yes. If he'd calculated this the easy way, the solution would have looked like this: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
You could as well take the log early on, if the shown way in the end leads to a log anyway.
Why is it so satisfying to draw the box around the answer?
Why so difficult? 3^2x = 333 is equivalent to 2x = log3(333) by logarithm definition itself. Then spread out 333 to 9*37, get 2x = log3(9) + log3(37), x = (2 + log3(37))/2 and finally x = 1 + log3(37)/2 Of course, it's useful to go the long way sometimes, but I've thought I do something wrong first. )))
Well, I got as far as "9^x has to be 333" and knowing that 9² is 81 and 9³ is 891 I just said "then x must be a little more than 2,5 = good enough for me" 😄 fast approx solution, I did calculate logarithms in school but never got attached to them, similar to integrals. I even had to do those in my oral exam, but never really got the hang of them, so naturally forgot all about their usage. They must have been easy, though, I did everything right and they just had one clarification question.
I mean does it need to be that long 😂😂😂. You could have solve it in less than 5 lines 😂😂. But thanks for the good old math, it brings me back to my college years.
....2.6433996 is as near as you will get in simple figures.😊
2.643399564
@@IPWCsInTheory Exactly. Good enough for me. So the poster here would still have to face a scientific calculator, or a log table. The long solution presented is therefore a futile exercise.
I find logs hard to follow. We got the answer for x but it is meaningless to me until I calculate a decimal equivalent afterwards. The abstract nature of calculus gives me the same fits. Geometry, trigonometry, and simple algrebra are not too bad though.
You dont need to calculate logs. There are tables which you can refer which makes it a lot easier.
@raviprakashvs1213 yes, it's been a long time since I've used them, but it's starting to return to me. Also, if I think about logs being inverse to exponents, then I can begin to visualize that, too.
Can't you just divide 999 by 3 and find base 9 log of 333?
Yup! But then the video would be a lot shorter and they'd rack up less watch time
Excelente explicación, paso a paso perfectamente explicado. Gracias
Más didáctico no podia ser ! Bravo!
Everything calculated correctly... great... What annoys me is the background music. It would also be nice if you wrote that X=2.6434. It's a thumbs up from me.
Why didn't you take log with base 3? I think this is the best simplification because we now don't want a approximated value.
Inefficient.
Very
or simpler: X = 1 + log9( 37 ).
the very case when the result is longer and more incomprehensible than the original task
Knowing if your computer program that solves maths for users works properly
If done right, this video would only have been about about 15 seconds long: 3(9^x) = 999 9^x = 333 ln(9^x) = ln(333) x * ln(9) = ln(333) x = ln(333)/ln(9) ≅ 2.6434
Great work man. And perfect speed. People dont get the fact that everyone is different. Mathematically half the people are below median intelligence, so that might be the reason. Subscribed.
Hey what device do you use for filming?
I found all three. They’re right next to the 9’s.
A lot of unnecessary steps
I agree very slow
Wow, I’m not really sure I see the point of that exercise. The reduction to 9^x=333 was so obvious, I thought it would be your starting point; then 333/9 = 37 (x is not a whole number so 2). I’d iterated that out to roughly 2.6433997 (somehow kind of thought you’d lead me to a round number) before you churned out a log equation.
2,6434 more correct :))
@@borisoff409 Maybe in Europe, but here in the U.S. you’re off by several orders of magnitude!
For teaching purpose is ok，could start by 3x9^2=243, 3x9^3=2187, so x should btw 2 and 3，and 3x9^2.5=3x9^2x9^(1/2)=729, so move further to x is btw 2.5 and 3 ，without cal and table the answer is 2.5
2,6434
Assume x = 1 n then drop + signs... Problem solved!!!😁😂😊😄🤩
I thought the answer should be integer.
What is the point of just simplicifaction, if the answer still sits with a log expression. Ultimately, one would wish to arrive at a pure numerical value. Therefore, you still need a calculator or a log table. In that case, it would only take 4 lines to arrive at the final value. (Signed: an old non-scientific, non-math guy, riddled with arthritis, but still with a working brain.)
Shorter: 3*9^x = 999 9^x = 333= 9*37 therefore 9^(x-1) = 37 I get x-1 = log 37÷ log 9 or X= 1 + log37/ ( 2* log 3)
.... = 1 + LOG (base 3) [ SQRT(37) ] ...
True. And if the base = 9, X = 1 + log9(37) / log9(9) = 1 + log9(37).
Great Math Solution!!!
Не получилось решить? Ну, может тогда на калькуояторе...
If I calculated this slowly, I would still be in 5th grade.
Gosto muito dessas explicações. Porém, nesse caso específico, o resultado encontrado não ajuda muito sem uma calculadora ou tábua de logaritmos. Mas, se fosse pra usar um ou outro, poderia ter resolvido sem fazer nada disso. Muito obrigado
I had to downvote. the title suggests an interesting problem that might have an elegant solution, maybe even no calculator required. After three lines of slightly slick transformation, it became a recap of logarithmic laws in slow motion landing at a calculator solution.
You expect me, the reader, to know logs & logs to base 3, but you take me thru those basic school processes of simplification? LoL 😂. It could be done in ¼ the steps & ¼ the time.
Merci. Très bien expliqué
This was the most agonizing 6 centuries-sorry I meant MILLENNIA of my life. The most efficient approach is the simplest, most convenient and fastest: 9^x + 9^x + 9^x = 999 9^x • 3 = 999 9^x = 333 x = log_9(333). This literally only took 3 steps to calculate other than just copying the problem down. Unbelievable. Go formulate 2 brain cells to rub together.
Basically writing the solution to one equation in terms of the solution to another, because log_3 37 is just the solution to 3^y = 37.
At this point just divide it all by 2 right away, or simplify it even more.
A simple question. Brought me to my school years
I solved it to 4 significant figures just by punching in 9 to the power of various "X's" in an old business HP RPN calculator to get 333 in less than 1/4 the time you took to write all of that - without providing an actual numerical answer. I now forget what I had but it was something like 2.6433 and I didn't go any further. I believe I could have solved it directly to more significant digits in less time if I had my engineering scientific HP calculator on my desk (its in my briefcase).
yep, did the same thing. Took about 1 minute. Got it to 4 decimals.
Да, всё правильно. Если в ответе остаются знаки математических операций - такой ответ ничего не стоит
It easy very easy for a experienced guy in aproach The correct logarithm of that..,..The bases are equal..,
@@user-wf1es2lp9s That would have required me to have my engineering calculator available as only it has log functions on it. As an engineer I look for the fastest way to solve a problem. Not necessarily the most elegant way. As a result math problems are often solved more quickly with simple calculation attempt methods as I used above. Now real engineering issues can take weeks of work to come up with a good approach and a likely range of solutions; then you pick the best choice (and document why you picked that one - as you don't always pick right).
с начала было более приятным когда не знали значение х, чем когда знали значение что ровна какому то не знаю чего😁😁😁
You can solve that equation in 2 steps, divide both sides by 9 to give 3x then divide 111 by 3 to give x = 37!!!
Nice
А в цифрах есть ответы? Какю цифру вместо "x" поставить нужно?
X = 1 + ln(37)/2 ln(3)
True. But a simpler equivalent equation is: x = ln(333)/ln(9)
I would say: 3(9^x) = 999 9^x = 333 e^(ln9)x = e^ln333 (ln9)x = ln333 x = ln333/ln9 = 2.6433
Можно было сразу сократить 3^2x=333 => 3^2x=3^2×37 => 3^x=37
I think the simplest answer to this Problem is x=log333 (base 9)
3 . 9^x = 999 9^x = 333 log (9^x) = log 333 x . log 9 = log 333 x = log (333) / log (9)
2.644 is approximate answer
Where did you get log ( 3 .37) where dud yiu get this 37 from??😮
111/3= 37
333/9 = 37.
К чему такие длиные выводы, если можно сразу находить логарифм от 37 по основанию 9 +1 или есть таблицы логарифмов с онованием 3. Всё равно надо брать таблицу натуральных логарифмов и ln37/ln9+1=приблизительно 2,64
Is there a point not stopping at x=log333/log9 ?
How do calculate the log of base 3 of a number?
Whit a log table. Or with a calculator.
log(x) / log(3)
Basically you don't.
Calculators and computers only provide bases e and 10, so you have to convert to one of those. The standard way is to convert everything to base e, using this formula: log[b](a) = log[e](a)/log[e](b). Calculators usually call log[e] "ln", but many programming languages call it just "log". More specifically, the problem in this video should have been done like this: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
I don't think it was clear. I meant, use the base change property: log of "n" in base "b" = log of "n" in base 10, divided by log of 3 in base 10. Or, base "e" if you prefer.
2,6434 would be good enought. Aproximation seems way simplier anyway, but good thought process thou.
And the additional step of showing the actual answer is not included because...?
One equation in one unknown .. 10 secs at most
Took me 15 seconds. But then, I'm rusty at math. As for the guy in the video, he's obviously much _more_ rusty, as he never does find the correct answer: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
How can log(111) be equivalent with log (3.37) Please explain it to me!
very good. thanks
Basta applicare la definizione di logaritmo dall'esponenziale e' x uguale a log in base 9 di 333.
Ответ еще страшнее выглядит чем дано
En la última parte simlifica sin hacer facror común, me parece que esta mal
So the short answer is you don't know the answer?
Sir can't we solve it without using logarithm?
Lord help us.
Did it my head within a couple of seconds
Why do you write 1+1+1=3
See logarithms ARE useful after all 3(9^x) = 999 9^x = 333 x = log(333)/log(9) ~2.6434
Aw, but then his video would only have been 15 seconds long and where's the ad revenue in that? 😉
Btw some ppl like me only see videos while muting the audios, thus every step helps 🤷♀️
Самое сложное было понять, что это 9, а не q
Why does he write the "7" without the stick?
Divide all by 9 and you arrive to 2(x-1)log3 = log 37
I'd say nice concept of "Simplification" 😅
If you don’t know the answer, just say so.
Where is part 2
How a bout classical music, maybe Vivaldi
請告訴我們，解這種問題在現實生活中有何作用？實會了對人有何幫助？
生活中物理跟數學無處不在 你沒用到不代表他不重要 如果大家都只會加減乘除買東西用 那這世界就不會是你現在看到的這樣
I’m gonna need a number. Does that equal a number?
If you have to use a calculator anyway, why not just stop at log9(333)? How is 1+0.5*log3(37) a better or simpler answer in anyway?
Calculators don't have log[9] buttons, so a more practical solution is as follows: 3(9^x) = 999 9^x = 333 ln(9^x) = ln(333) x * ln(9) = ln(333) x = ln(333)/ln(9) ≅ 2.6434
@@RobbieHatleywho's using a calculator? Surely it would be be an app or a computer program these days? And if a modern app doesn't have a "log base x of y" function, then it really ought to
@@douglaswolfen7820 : Re "Who's using a calculator": You can use a slide rule if you like, it's all the same to me (though not as easy). Re "ought to": If wishes were fishes we'd all own chains of lucrative seafood restaurants. 🙄 The fact remains, most calculators, apps, log tables, and computer programming languages don't have log[3], log[9], or log[n], just log[e] ("ln") and/or log[10], so it's advantageous to learn the base change formula: log[b](x) = ln(x)/ln(b), or just do everything using natural log from the start: 3(9^x)=999 9^x=333 ln(9^x)=ln(333) x*ln(9)=ln(333) x = ln(333)/ln(9) ≅ 2.64339956411...
@@douglaswolfen7820 : Re "ought to": woulda shoulda coulda. That's not the world we live in. In the world we live in, most (physical) calculators, calculator apps, web math sites and calculators, and computer programming languages, have logs to base e and 10 only. However, that's not a problem, because log[b](a) = ln(a)/ln(b), so only natural (base e) logarithms are needed. If this principle is applied to the problem at hand, it becomes easy to find both the exact answer and a decimal approximation, in about 15 seconds: 3(9^x) = 999 9^x = 333 x = log[9](333) x = ln(333)/ln(9) (exact answer) x ≅ 2.6434 (decimal approximation)
@@RobbieHatley huh. I just checked the one on my phone and you're right. I'm disappointed though
Right answer is X=2.6434. We all are calculat and find the answer is 2.6434 only.
My wife wants to know, what is this math used for?
Science and engineering usually
Found it... Its on top of the 9
Can u solve without logorithm?
No. It is an inherent part of solving for a variable exponent as logarithms are the inverse of exponentiation. (a common misconception is that taking the root of a value is the inverse of exponentiation, but actually the radical is just a fancy way to denote that the root value is the denominator of the exponent). So, to solve a^x=b, you can only isolate x to one side by taking the logarithm of both sides, getting x = log_a (b) after a bit of simplifying.
This problem involves logarithms pretty much by definition. You've got a base (9), you're raising it to an exponent (x) and you've got the result (333). You know the base, you know the result, and you're trying to find out what value the exponent has. That's what a logarithm _is_
It's right there 4 times shown on the screen.
The answer is more difficult.
4:25 How did log111 convert into log(3.37)? Hooow?
log(111)=log(3×37)=log(3.37)
@@Adrenalinclip you mean 3*37=3.37? 🤷♂️
Shouldn't there be an actual member at the end of all of this? Edit: number not member
From a certain point of view, the answer given _is_ a number. It's just a number written in a weird way And yes, sometimes you need to write it out as a traditional decimal number, like "2.6394747” or something. But there's a problem with that: the real number would be infinitely wrong, so you can only write an approximation, not the actual number. Sometimes it's better to just write down the calculation and stop there
How about x = log111/log9.
What’s wrong with 333 divided by 9 to give x ?
I don’t even understand the question ! Lol😂
Because it is incorrect. It is the 9th root off 333. Easier to do on a calculator than log3.
Everything.
That would yield 37, which is the wrong answer. (The actual value is about 2.6434) The correct solution is as follows: 3(9^x) = 999 9^x = 333 x = log[9](333) = ln(333)/ln(9) ≅ 2.6434
Фундаментальная ошибка их образования во всей красе. Ответ находится в два действия. А если нужно число, то его посчитает любой онлайн калькулятор. То есть сами себя загнали в глупые рамки и от математики не остается и следа.
you can also put a ring through your nose
So log base 3(999) = 2π, or log base 9(999) = π :)
Close! Within 1 part per thousand. Not exact, though. log[9](999) ≅ 3.1434 whereas π ≅ 3.1416
That many steps to get to 333?