Prove that the value of the following determinant is zero
`|(logx,logy,logz),(log2x,log2y,log2z),(log3x,log3y,log3z)|`

Integrate the following functions x log2x

Solve the following differential equations x log x (dy)/(dx) + y = 2/x log x

Find dy/dx of y=(xlogx)^log(logx)

Differentiate the following y=e^(2log tan5x)

Separate the intervals of monotonicity for the following functions. f(x) = (log_(e)x)^(2) + (log_(e)x)

Prove the following: int_1^3 dx/(x^2(x+1) = 2/3 +log(2/3)

Prove that log_(3) 2, log_(6) 2 , log_(12)2 are in H.P .

The domain of the function f(x)=log_2 (log_3 (log_4 x)) is

If the angle between the curves y=2^(x) and y=3^(x) is alpha , then the value of tan alpha is equal to a) (log((3)/(2)))/(1+(log2)(log3)) b) (6)/(7) c) (1)/(7) d) (log(6))/(1+(log2)(log3))