How do you find the domain, x intercept and vertical asymptotes of g(x)=log_6x?

Dec 5, 2017

Domain: $x > 0$, vertical asymptote: $x = 0$, $x$-intercept: $\left(1 , 0\right)$.

Explanation:

You cannot take the log of a negative number and there is no power to which you can raise 6 and get 0, so the domain is $x > 0$.

The vertical asymptote of a log function is at the end of its domain, so the vertical asymptote is $x = 0$.

To find the $x$-intercept we set ${\log}_{6} x = 0$

Solve we have:
${\log}_{6} x = 0 \setminus \rightarrow {6}^{0} = x \setminus \rightarrow x = 1$, so the $x$-intercept is $\left(1 , 0\right)$.