# How do you find the domain, x intercept and vertical asymptotes of y=log_10(x/5)?

Apr 21, 2018

See details below

#### Explanation:

$L o {g}_{b} x$ is a continous function and to define a real number the argument x need to be positive. Then in our case

$\frac{x}{5} > 0$. That means $x > 0$

Domain is $D o m \left(y\right) = \left(0 , + \infty\right)$

x intercept : We know that ${\log}_{b} x = 0$ only when $x = 1$. Then in our case $\frac{x}{5} = 1$. This occur only if $x = 5$

Vertical asymptotes : We also know that ${\lim}_{x \to 0} L o {g}_{b} x = - \infty$. Then in our case it is the same trend, so vertical asymptote is $x = 0$