#### Answer

$1.0791$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the Laws of Logarithms to find an equivalent expression for the given expression, $
\log_{10} 12
,$ which uses the given logarithmic values, $\log_{10} 2=
0.3010
$ and/or $\log_{10} 3=
0.4771
.$
$\bf{\text{Solution Details:}}$
The given expression can be expressed as
\begin{array}{l}\require{cancel}
\log_{10} (4\cdot3)
\\\\=
\log_{10} (2^2\cdot3)
.\end{array}
Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\log_{10} 2^2+\log_{10} 3
.\end{array}
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
2\log_{10} 2+\log_{10} 3
.\end{array}
Substituting the known values of the logarithmic expressions results to
\begin{array}{l}\require{cancel}
2(0.3010) 2+0.4771
\\\\=
0.6020 2+0.4771
\\\\=
1.0791
.\end{array}