Mathematical Olympiad | Learn how to solve exponential equation quickly | Math Olympiad Training

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Mathematical Olympiad | Learn how to solve exponential equation quickly | Math Olympiad Training

Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!

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[Maahi_xgod]

first view, frist like and also frist comment 💬
big fan of yours

[murdock]

Awesome challenge, amazing way to solve it, many thanks! 🙂
My way:
Do the ln → (x²/6) = ln(3)/ln(2) → x = +/-√(6(ln⁡(3)/ln⁡(2)) ≈ +/-3, 08379… 🙂
Or: raise given equation to a power (x/2) → x^((x^2/6)) = 3 →
2^x² = 3^6 = 729 → x^2 = ln(729)/ln(2)

[ArhMatBenzamene]

Your theoretical breakdown is superb. I don't suppose you would consider doing a physical application demonstration of your lessons? I am a marine engineer and i've not had to do additional mathematics for a very long time, beside teaching a younger cousin some basic calculus 😀 i have been able to demonstrate the daily use for my line of work with tank measurement to area and volume but those are still very basic quadratic equations

[HappyFamilyOnline]

Another great video👍
Thanks for sharing🌺

[williamwingo]

Here's a different approach using the calculus identity _a^x = e^(x ln a), _ which I'm discovering works pretty good with quite a few of these type problems:

2^(x/3) = 3^(2/x); substitute the above expression for each side,
e^((x/3)(ln 2)) = e^((2/x)(ln 3)); take ln of each side to get rid of the "e's, "
(x/3)(ln 2) = (2/x)(ln 3); multiply both sides by 3,
x ln 2 = (6/x) ln 3; multiply both sides by x,
(x^2) ln 2 = 6 ln3; divide both sides by ln 2,
x^2 = 6 ln 3 / ln 2; take square roots of each side, and voila!
x = +/-- sqrt(6 ln 3 / ln 2); and a quick trip to the calculator gives us
x = +/-- 3.08379, approximately.
Elapsed time: less than 60 seconds.
Check:
2^(3.08379 / 3) = 2.039096;
2^(2 / 3.08379) = 2.039099.
2^(--3.08379 / 3) = 0.490413;
2^(2 / --3.08379) = 0.490414.
Thank you, ladies and gentlemen, I'm here all week. 🤠

[mathsplus]

Really nice and clear maths solution. Thank you Sir.

[randomjudgements]

Wow very nice Idea to use log in the first place 😀

[owlsmath]

Cool! Did the same...solve by logs :)

[hii]

Thank you sir please share more log problems

[mykiits]

Another way to solve:
1. Raise given eq to a power 3x. We obtain eq: 2^(x^2)=729
2. Take log base 2 on both sides
3. Take sqrt on both sides. Answer will be exactly the same as in video

[wbtittle]

sqrt( 6 (ln 3 / ln 2) ) ... Did we get anything more from the extra steps? I like that you reminded me about the ln 3/ ln2 ==> definition of ln(base2) 3 ...

A definition I learned a year after I needed it the first time.

[bigm]

Thank goodness for logarithms, Professor!😀

[j.c]

Is there a solution without using log?

[giuseppemalaguti]

x=+sqrt(log(2)729)....=+3, 0837923....anche la soluzione negativa è ok