Evaluate :

`log( a^x/b^x ) + log ( b^x / c^x ) + log( c^x / a^x )`

Evaluate: int(1)/(x log x log(log x))dx

The value of int(1)/(x+x log x)dx is 1+log x(b)x+log x(c)x log(1+log x)(d)log(1+log x)

If log_(a)x = m and log_(b)x =n then log_(a/b) x= ______

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

If x = log_(c) b + log_(b) c, y = log_(a) c + log_(c) a, z = log_(b) a + log_(a) b, then x^(2) + y^(2) + z^(2) - 4 =

If a^(x), b^(x) and c^(x) are in GP, then which of the following is/are true? (A) a, b, c are in GP (B) log a, log b, log c are in GP (C ) log a, log b, loc c are in AP (D) a, b, c are in AP

int(1)/(1+e^(x))dx= (a) log(1+e^(x)) (b) log((1+e^(x))/(e^(x))) (c) log(1+e^(-x)) (d) -log(e^(-x)+1)