Solve `x^((log)_y x)=2a n dy^((log)_x y)=16`

Solve: 1/4x^(log_2sqrt(x))=(2. x^((log)_2x))^(1/4)

Solve (log)_x2(log)_(2x)2=(log)_(4x)2.

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

Solve: |x-1|^((log)_(10)x)^2-(log)_(10)x^2=|x-1|^3

Solve 4^((log)_9x)-6x^((log)_9 2)+2^((log)_3 27)=0

Solve for: x :(2x)^((log)_b2)=(3x)^((log)_b3) .

Solve : 2(log)_3x-4(log)_x 27lt=5 (x >1)

Solve (log)_4 8+(log)_4(x+3)-(log)_4(x-1)=2.

If y=a^(1/(1-(log)_a x)) and z=a^(1/(1-(log)_a y)) ,then prove that x=a^(1/(1-(log)_a z))

Solve: x(dy)/(dx) + 2y -x^(2) log x=0