#### Answer

$0.7781$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}