# Exponential function

*y*=*a*.^{x}*a*> 1Domain â†’

*R*; Range â†’ (0, âˆž)**(a)**

**(b)**

# Logarithmic function

Logarithmic function is inverse of exponential function. Hence domain and range of logarithmic functions are range and domain respectively of exponential function.

Also graph of function can be obtained by taking the mirror image of the graph of the exponential function in the line

*y*=*x*.*y*= log_{a}*x*,*a*> 0 and â‰ 1.Domain â†’ (0, âˆž); Range â†’ (â€“ âˆž, âˆž)

**(a)**

**(b)**

# Properties of logarithmic function

**For**

*x*,*y*> 0- log
(_{a}*x*.*y*) = log+ log_{a}x_{a}y - log
(_{a}*x*/*y*) = logâ€“ log_{a}x_{a}y - log
_{a}_{ }(*x*) =^{b}*b*log_{a}x - If log
>log_{a}xâ‡’_{a}y - If log
=_{a}x*y*â‡’*x*=*a*^{y} - If log
>_{a}x*y*â‡’ - log
=_{y}x - log
> 0 â‡’_{a}x*x*> 1 and*a*> 1 or 0 <*x*< 1 and 0 <*a*< 1