Solve `sqrt(log_x(a x)^(1/5)+log_a(a x)^(1/5))+sqrt(log_a(x/a)^(1/5)+log_x(a/x)^(1/5))=a`

Solve log_5(5^(1/x)+125)= log_5 6+1+1/(2)x .

Lt_(x to 1)(log_(5)5x)^(log_(x)5)=

Solve for x:log_(5)(5^(1//x)+125)=log_(5)6+1+1//2x

2log_(2)(log_(2)x)+log_((1)/(5))(log_(2)2sqrt(2x))=1

Solve for x, log_(x) 15 sqrt(5) = 2 - log_(x) 3 sqrt(5) .

Solve : log_(5)(x + 1) - 1 = 1 + log_(5)(x - 1) .

log_5 ((2+x)/10)=log_5 (2/(x+1))

Solve log_(5)sqrt(7x-4)-1/2=log_5sqrt(x+2)

Solve log_(x)3+log_(3)x=log_(sqrt(3))x+log_(3)sqrt(x)+(1)/(2)

Let P=(5)/((1)/(log_(2)x)+(1)/(log_(3)x)+(1)/(log_(4)x)+(1)/(log_(5)x))and (120)^(P)=32 , then the value of x be :