Answer
$g(x)=\log_6x$
Work Step by Step
Substituting values of $x$ in the given function, $
g(x)=\log_6x
$, results to
\begin{array}{c|c|c}
\text{If }x=1: & \text{If }x=6 & \text{If }x=36
\\\\
g(x)=y=\log_6x & g(x)=y=\log_6x & g(x)=y=\log_6x
\\
y=\log_6 1 & y=\log_6 6 & y=\log_6 36
\\
y=0 & y=1 & y=\log_6 6^2
\\
&& y=2\log_6 6
\\
&& y=2(1)
\\
&& y=2
.\end{array}
Tabulating the results above gives the table below.
\begin{array}{c|c}
\hline
x & y
\\\hline
1 & 0
\\\hline
6 & 1
\\\hline
36 & 2
\end{array}
Connecting the points $
\left(1,0\right),
\left(6,1\right),
\text{ and }
\left(36,2\right)
$ with a curve gives the graph of $
g(x)=\log_6x
$.
