Answer
$2.745$
Work Step by Step
Using the properties of logarithms, the given expression, $
\log_b 45
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_b (3^2\cdot5)
\\\\=
\log_b 3^2+\log_b5
\\\\=
2\log_b 3+\log_b5
.\end{array}
Since it is given that $\log_b 3=0.792 $ and $\log_b5=1.161$, the expression above, $
2\log_b 3+\log_b5
,$ evaluates to
\begin{array}{l}\require{cancel}
2(0.792)+1.161
\\\\=
2.745
.\end{array}
