Bolivia | A Nice Algebra Problem | Math Olympiad

[@LITHICKROSHANMS-gw2lx]

Nice solution sir

[@SALogics]

Thanks and welcome! ❤

[@raghvendrasingh1289]

Nice problem Third method Let log x ( base5) = y then x= 5^y Putting in equation (5^y)^y = 5^ 4 5^(y^2) = 5^4 hence y^2 = 4 or y = 2 , -2 now x= 5^y x = 25 , 1/25

[@SALogics]

Very nice! ❤

[@SGuerra]

Que que você fez uma questão bonita. Parabéns 👏👏👏👏👏

[@SALogics]

muito obrigado! ❤

[@ZionV-d5m]

Excelente solución

[@SALogics]

Thanks and welcome! ❤

[@ВладимирКоваленко-щ6д]

Если знать таблицу квадратных чисел, то такую задачу можно решить за несколько сикунд 25^2=625

[@SALogics]

ты прав! ❤

[@ChavoMysterio]

x^[log_5(x)]=625 [5^[log_5(x)]]^[log_5(x)]=625 Let n=log_5(x) (5ⁿ)ⁿ=625 5^(n²)=5⁴ n²=4 |n|=2 n=-2 log_5(x)=-2 x=5^-2 x=0.04 ❤ n=2 log_5(x)=2 x=25 ❤

[@SALogics]

Very nice trick! ❤

[@prollysine]

log(5)x * log(5)x = log(5)625 , 5^4=625 , log(5)625=4 , (log(5)x)^2=2^2 , log(5)x=+/-2 , x= 5^2 , 5^(-2) , x= 25 , 1/25 ,

[@SALogics]

Very nice trick! ❤

[@prollysine]

@@SALogics Thanks!

[@DJ.Nihad6174]

First method >>>>>>

[@SALogics]

Very nice! ❤

[@trojanleo123]

x = (25 , 1/25)

[@SALogics]

You are right! ❤

[@-basicmaths862]

Answer=25

[@SALogics]

Yes, 25 and 1/25

[@yakupbuyankara5903]

X=25

[@SALogics]

You are right! ❤