#### Answer

$x\approx3.322$

#### Work Step by Step

Taking the logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $
2^x=10
,$ is
\begin{array}{l}\require{cancel}
\log2^x=\log10
\\\\
x\log2=\log10
\\\\
x=\dfrac{\log10}{\log2}
\\\\
x\approx3.322
.\end{array}