Answer
$0.1761$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Laws of Logarithms to find an equivalent expression for the given expression, $
\log_{10} \dfrac{3}{2}
,$ which uses the given logarithmic values, $\log_{10} 2=
0.3010
$ and/or $\log_{10} 3=
0.4771
.$
$\bf{\text{Solution Details:}}$
Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\log_{10} 3-\log_{10} 2
.\end{array}
Substituting the known values of the logarithmic expressions results to
\begin{array}{l}\require{cancel}
0.4771-0.3010
\\\\=
0.1761
.\end{array}
