# How do you graph g(x)= log_6 x?

Using that ${\log}_{6} \left(x\right)$ is defined to be the value such that ${6}^{{\log}_{6} \left(x\right)} = x$, we can find points to plot by using that
$g \left({6}^{k}\right) = {\log}_{6} \left({6}^{k}\right) = k$ for any choice of $k$. For example, we would have points such as $\left(1 , 0\right) , \left(6 , 1\right) , \left(36 , 2\right)$ as well as $\left(\frac{1}{6} , - 1\right) , \left(\frac{1}{36} , - 2\right)$.
In general, logarithmic functions tend to $- \infty$ as $x$ approaches $0$, so we have a vertical asymptote at $x = 0$. After that, you can use some easily plotted points such as the ones above to see approximately how the curve grows. In this case, the graph will be as follows: