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

Prove log_(b)b = 1

Prove log_(b) 1=0

The maximum value of (log_(e)x)/(x) , if x gt0

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

Prove that int_(a)^(b) f(x)dx= int_(a)^(b) f (a+b-x)dx" hence evaluate " int_(0)^(pi/4) log(1+tan x)dx .

If y = log_(x) (log x) then (dy/dx)_(x = e) =

The solution set of log_(x)2 log_(2x)2 = log_(4x) 2 is :

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx and hence evaluate int_(0)^(pi//2)(2log sin x-log sin2x)dx .

The number of solutions of : log_(4) (x - 1)= log_(2) (x - 3) is :

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