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! ❤