## College Algebra (11th Edition)

$x=1$
$\bf{\text{Solution Outline:}}$ 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}