Answer
$x=\pm6$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log_3(x^2-9)=3
,$ convert to exponential form. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $\log_by=x$ is equivalent to $y=b^x$, the equation above, in exponential form, is equivalent to
\begin{array}{l}\require{cancel}
x^2-9=3^3
\\\\
x^2-9=27
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x^2=27+9
\\\\
x^2=36
\\\\
\sqrt{x^2}=\pm\sqrt{36}
\\\\
x=\pm\sqrt{(6)^2}
\\\\
x=\pm6
.\end{array}
