# How do you find the domain and range of  y = log_5x?

Jul 19, 2015

$f \left(x\right) = {\log}_{5} x$ is the inverse of the function $e \left(x\right) = {5}^{x}$
which has domain $\left(- \infty , \infty\right)$ and range $\left(0 , \infty\right)$.

So the domain of ${\log}_{5} x$ is $\left(0 , \infty\right)$ and range is $\left(- \infty , \infty\right)$

#### Explanation:

The domain of $e \left(x\right) = {5}^{x}$ is the whole of $\mathbb{R}$, that is $\left(- \infty , \infty\right)$, but its range is $\left(0 , \infty\right)$.

So the domain of its inverse $y = {\log}_{5} x$ is $\left(0 , \infty\right)$ and its range is $\left(- \infty , \infty\right)$