A nice Math Olympiad Logarthms | Exponent Simplification | Find the Value of x ? |

Math Olympiad Logarthms | Exponent Simplification
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[@rainerzufall42]

3:37 Where did you get the third power from? That came out of nowhere!

[@superacademy247]

It's an error! It should be second power

[@rainerzufall42]

@@superacademy247 Yeah, you didn't use it, just a typo!

[@superacademy247]

Absolutely

[@michaelhuppertz6738]

Third method set right side to 3^4 and apply to both side log base 3 this gives you: log3(x) * log3(x) = log3(3) * 4 which is equal to log3(x)*log3(x) = 4. Now it's clear that the result log3(x) must result to 2 or -2 to match the right side. To get that you use log3(a^b) = b*log3(a) and a becomes 3 and b has to be 2 or -2.

[@rimmir6504]

Much faster method👍

[@MrGeorge1896]

The easiest way by far is to apply log3() on both sides: x ^ log3(x) = 81 log3(x ^ log3(x)) = log3(81) = 4 log3(x) ^ 2 = 4 log3(x) = ±2 x = 3 ^ ±2 = 9 v 1/9

[@rainerzufall42]

Yeah, same idea.

[@rainerzufall42]

"Apply {} to both sides" - be careful! This doesn't work with every function. Well, log is monotone and has an inverse function, so everything is okay...

[@SidneiMV]

x = 3^u (3^u)^u = 3⁴ 3^(u²) = 3⁴ u² = 4 => u = ± 2 u = 2 => x = 9 u = -2 => x = 1/9

[@user-qy8re3yx3d]

x=9, легко решается логарифмированием по основанию 3.

[@superacademy247]

Base 3 logarithm looks amazing 😄 Thanks 👍💯

[@rainerzufall42]

Quick thoughts: Bring it all to base 3: 81 = 3^4, x = 3^(log_3(x)). Thus 3^(log_3(x))^(log_3(x)) = 3^(log_3(x) * log_3(x)) = 3^4 => (log_3(x))^2 = 4 => log_3(x) = +/- 2 => x = 3^(+/- 2) = { 9, 1/9 }. Test: 9^(log_3(9)) = 9^2 = 81. (1/9)^(log_3(1/9)) = (1/9)^-2 = 81.

[@NishkarshPandey-go5sh]

Class 11 easy question for jee aspirant 😂😂🥱

[@user-ee7nw2rx9s]

Что такое log3, по какой базе? Почему бы не логарифмировать по базе 3 В итоге получается уравнение элементарное квадратное уравнение (log(3)x)^2=4 log(3)x= 2 или - 2 По определению логарифма х=3^2=9 или х=3^(-2)=1/9 Все решение занимает 1-2 минуты

[@xgx899]

Exactly, too many words and equations for a trivial problem.

[@ludmilak9396]

Чрезвычайно некорректно! log and ln -- это логарифмы по неодинаковым основаниям! Минус вам!

[@ludmilak9396]

Вообще какая-то халтура

[@user-sx6vo6ne5f]

za dużo piszesz, pismaku !