`y=2^(1/((log)_x4)`, then find x in terms of y.

If (log)_2y=xa n d(log)_3z=x , find 72^x in terms of yand zdot

If log_(3) y = x and log_(2) z = x , " find " 72^(x) in terms of y and z.

If log_(10) x = y ," then find "log_(1000)x^(2)" in terms of " y .

"If "log_(e)(log_(e) x-log_(e)y)=e^(x^(2_(y)))(1-log_(e)x)," then find the value of "y'(e).

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

If y= cos^(-1) x , Find (d^(2)y)/(dx^(2)) in terms of y alone.

If log_(5) x = a and log_(2) y = a ," find "100^(2a-1) in terms of x and y .

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .