#### Answer

$x=1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log_{10}(\log_2 2^{10})=x
,$ use the properties of logarithms.
$\bf{\text{Solution Details:}}$
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent
\begin{array}{l}\require{cancel}
\log_{10}(10\log_2 2)=x
.\end{array}
Since $\log_b b =1,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\log_{10}(10\cdot1)=x
\\\\
\log_{10}10=x
\\\\
1=x
\\\\
x=1
.\end{array}