Can you pass College Entrance Aptitude Test ? || Find x=?

[@ericmariaud8237]

Pourquoi faire simple quand on peut faire compliqué ?
x>0
log_3( x^( log_3( x ) ) = log_3( 81 )
( log_3( x) )² = log_3( 3⁴)
( log_3( x) )² = 4
| log_3( x) | = 2
log_3( x) = 2 ou log_3( x) = -2
x = 3² ou x = 3^(-2)
x = 9 ou x = 1/9

[@Sergey_Moskvichev]

This is the simplest and most rational way: to prolog both parts by base 3.

[@ericmariaud8237]

@@Sergey_Moskvichev Thanks

[@RyanLewis-Johnson-wq6xs]

X^(Log[3,X])=81 X=0.1 recurring=1/9 X=9

[@prollysine]

log(3)x * log(3)x=log(3)81 , log(3)81=4 , log(3)x * log(3)x = 4 , --> log(3)4 * log(3)4 = 2 * 2 ,
log(3)x=2 , --> , x=3^2 , x =9 , test , 9^log(3)9=9^2 , 9^2=81 , OK ,

[@maherom1]

Please Can you solve this équation
sqrt (x-1) +4 sqrt(y-4) = (x+y)/2

[@maherom1]

We suppose a= sqrt(x-1) , b= sqrt(y-4) finnaly WE get (a-1)^2 +(b-4)^2 = 12 ......

[@maherom1]

Thanks i solved it

[@user-tu1vn4sh5t]

I just guessworked this lol

[@superacademy247]

Don't guess . Put in some works!🥰

[@key_board_x]

x^{Log[3](x)} = 81
x^{Ln(x) / Ln(3)} = 81
Ln[x^{Ln(x) / Ln(3)}] = Ln(81)
[Ln(x) / Ln(3)].Ln(x) = Ln(81) → let: a = Ln(x)
[a / Ln(3)].a = Ln(81)
a² / Ln(3) = Ln(81)
a² = Ln(3) * Ln(81)
a² = Ln(3) * Ln(3⁴)
a² = Ln(3) * 4.Ln(3)
a² = 4 * [Ln(3)]²
a² = [2.Ln(3)]²
a = ± 2.Ln(3)
a = ± Ln(9) → recall: a = Ln(x)
Ln(x) = ± Ln(9)
First case: Ln(x) = Ln(9)
x = 9
Second case: Ln(x) = - Ln(9)
Ln(x) = - Ln(9)
Ln(x) = Ln(9)^(- 1)
x = 9^(- 1)
x = 1/9