Find the range of `f(x)=(log)_e x-((log)_e x)^2/(|(log)_e x|)`

Find the range of f(x)=log_e x-((log_e x)^2)/(|log_e x|).

Find the range of f(x)=cos((log)_e{x})dot

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these

Find the area bounded by y=-(log)_e x , y=(log)_e x ,y=(log)_e(-x),a n dy=-(log)_e(-x)dot

Evaluate: int(e^(5\ (log)_e x)-e^(4\ (log)_e x))/(e^(3\ (log)_e x)-e^(2\ (log)_e x))\ dx

Evaluate: int(e^(6\ (log)_e x)-e^(5\ (log)_e x))/(e^(4\ (log)_e x)-e^(3\ (log)_e x))\ dx

Separate the intervals of monotonocity for the function f(x)=((log)_e x)^2+((log)_e x)

If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)_e y)/(x(1-y(log)_e x(log)_e y)

If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)_e y)/(x(1-y(log)_e x(log)_e y)

Find fog and gof , if f(x)=e^x , g(x)=(log)_e x