Question

In the following exercises, solve each logarithmic equation.

$y={\log }_{\frac{1}{3}}\left(x\right)$

Short answer

The graph is

Step-by-step solution

Given information

Given the function$y={\log }_{\frac{1}{3}}\left(x\right)$

Rewriting in exponential form

Rewriting, we get

$$\begin{gathered} y={\log }_{\frac{1}{3}}\left(x\right) \\ {\left(\frac{1}{3}\right)}^y=x \end{gathered}$$

Use the point plotting method

Using point plotting, we get

$y$	${\left(\frac{1}{3}\right)}^y=x$	$(x,y)$
$0$	$1$	$(1,0)$
$-1$	$3$	$(3,-1)$
$1$	$\frac{1}{3}$	$(\frac{1}{3},1)$

Sketching the graph by plotting points

Plotting the points, we get