## College Algebra (11th Edition)

$0.7781$
$\bf{\text{Solution Outline:}}$ Use the Laws of Logarithms to find an equivalent expression for the given expression, $\log_{10} 6 .$ Then substitute the given logarithmic values, $\log_{10} 2= 0.3010$ and $\log_{10} 3= 0.4771 ,$ as necessary. $\bf{\text{Solution Details:}}$ Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the given expression is equivalent \begin{array}{l}\require{cancel} \log_{10} (2\cdot3) \\\\= \log_{10} 2+\log_{10} 3 .\end{array} Substituting the known values of the logarithmic expressions results to \begin{array}{l}\require{cancel} 0.3010+0.4771 \\\\= 0.7781 .\end{array}