Answer
Graph of $g(x)=\log_{1/3}x$
Work Step by Step
Since $y=\log_b x$ implies $
x=b^y
,$ the given function, $
g(x)=\log_{1/3}x
$, implies
\begin{align*}
y&=\log_{1/3}x
\\
(1/3)^y&=x
.\end{align*}
Substituting values of $y$ in the equation above results to
\begin{array}{c|c|c}
\text{If }y=-1: & \text{If }y=0 & \text{If }y=1
\\\\
(1/3)^y=x & (1/3)^y=x & (1/3)^y=x
\\
(1/3)^{-1}=x & (1/3)^0=x & (1/3)^1=x
\\\\
3=x & 1=x & \dfrac{1}{3}=x
.\end{array}
Tabulating the results above results to the table below.
\begin{array}{c|c}
\hline
x & y
\\\hline
3 & -1
\\\hline
1 & 0
\\\hline
\dfrac{1}{3} & 1
\end{array}
Connecting the points $
\left(3,-1\right),
\left(1,0\right),
\text{ and }
\left(\dfrac{1}{3},1\right)
$ with a curve gives the graph of $
g(x)=\log_{1/3}x
$.
