Show that `f(x)=(log)_a x ,\ \ 00` .

Show that f(x)=(log x)/(x), x ne 0 is maximum at x = e .

Show that 'f(x)=(log)_(-)ax,backslash backslash00^(@)

Show that f(x) = log [x + sqrt(1 + x^2)] is a odd function.

Show that the logarithmic function f: R0+->R given by f(x)=(log)_a x ,\ a >0 is a bijection.

Show that f(x, y)=x-y log y+y log x is a homogeneous function of x and y.

Show that the logarithmic function f: R0+vecR given by f(x)=(log)_a x ,a >0 is bijection.

Write the set of values of ' a ' for which f(x)=(log)_a x is increasing in its domain.

Write the set of values of ' a ' for which f(x)=(log)_a x is decreasing in its domain.

Prove that the function f(x)=(log)_a x is increasing on (0,oo) if a >1 and decreasing on (0,oo), if 0ltalt1