`f(x)= log_(e)x`, find value of `f(1)`

If f(x)=log_(x)(log_(e)x) , then the value of f'(e ) is -

If f (x) = cos (log_e x) , find the value of : f(x) f(y)-1/2[f(x/y)+f(xy)] .

If f(x) = cos(log_e x) , then find the value of f(x) cdot f(y) - 1/2[f(x/y) + f(xy)]

If f(x)=log_x(logx) then the value of f'(e) is

IF f(x)= log_x(logx) then the value of f'(e) is

If f'(x)=f(x)+ int_(0)^(1)f(x)dx , given f(0)=1 , then find the value of f(log_(e)2) is

For x>0, let f(x)=int_(1)^(x)(log t)/(1+t)dt. Find the function f(x)+f((1)/(x)) and find the value of f(e)+f((1)/(e))

If f(x)=e^x and g(x) =log_(e)x, then find (f+g)(1) and fg(1).

If f(x)=log_(10)x and g(x)=e^(ln x) and h(x)=f [g(x)] , then find the value of h(10).

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot