# Exponential function

*y*=*a*.^{x}*a*> 1Domain â†’

*R*; Range â†’ (0, âˆž); Nature â†’ non-periodic, one-one, neither odd nor even, monotonically increasing,**(**; monotonically decreasing,*a*> 1)**(0 <***a*< 1)# Logarithmic function

Logarithmic function is inverse of exponential function.Hence domain and range of the logarithmic functions are range and domain respectively of exponential functions. Also graph of a 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); Period â†’ nonâ€“periodic; Nature â†’ neither odd nor even; Interval which the inverse can be obtained â†’ (0, âˆž)

# Properties of logarithmic function

- log
(_{a}*x*â‹…*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‡’ - log
=_{y}x