Prove
`log_(x)b^(x)=x`

Prove log_(b)b = 1

Prove log_(b) 1=0

If log_(y)x +log_(x)y = 7 , then the value of (log_(y)x)^(2) +(log_(x)y)^(2) , is

If x= e^((x)/(y)) , then prove that (dy)/(dx)= (x-y)/(x.log x)

if x^(2) + y^(2)= 25xy , then prove that 2 log(x + y) = 3log3 + logx + logy.

If x^2 + y^2 = 6xy , prove that 2 log (x + y) = logx + logy + 3 log 2

Solve for x if log(x-1)+log(x+1)=log1

The possible value(s) of x, satisfying the equation log_(2)(x^(2)-x)log_(2) ((x-1)/(x)) + (log_(2)x)^(2) = 4 , is (are)

Prove that int_(0)^(1)log((1)/(x)-1)dx=0 .

Method of integration by parts : If int log(x^(2)+x)dx=x log(x^(2)+x)+A then A=.....