Answer
$x=3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log_2(x^3+5)=5
,$ 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^3+5=2^5
\\\\
x^3+5=32
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x^3=32-5
\\\\
x^3=27
\\\\
x=\sqrt[3]{27}
\\\\
x=\sqrt[3]{3^3}
\\\\
x=3
.\end{array}