College Algebra (11th Edition)

$12$
$\bf{\text{Solution Outline:}}$ Use the properties of logarithms to simplify the given expression, $\log 10^{12} .$ $\bf{\text{Solution Details:}}$ Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent \begin{array}{l}\require{cancel} 12\log 10 .\end{array} Since $\log_b b=1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 12\log_{10} 10 \\\\= 12(1) \\\\= 12 .\end{array}