Question

In the following exercises, solve each logarithmic equation.$y={\log }_{1.5}\left(x\right)$

Short answer

The graph is

Step-by-step solution

Given information

Given the function$y={\log }_{1.5}\left(x\right)$

Rewriting in exponential form

Rewriting in exponential form, we get

$$\begin{gathered} y={\log }_{1.5}\left(x\right) \\ {(1.5)}^y=x \end{gathered}$$

Using the point plotting method

Using the point plotting, we get

$y$	${(1.5)}^y=x$	$(x,y)$
$0$	$1$	$(1,0)$
$-1$	$\frac{2}{3}$	$(\frac{2}{3},-1)$
$1$	$1.5$	$(1.5,1)$

Sketch the graph by plotting points

Plotting the points, we get