Answer
$3b$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To write the given expression, $
\ln27
,$ in terms of $a$ and $b,$ where $a=\ln2$ and $b=\ln3,$ use the laws of logarithms and substitution.
$\bf{\text{Solution Details:}}$
The given expression is equivalent to
\begin{array}{l}\require{cancel}
\ln3^3
.\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}
3\ln3
.\end{array}
By substitution, since $b=\ln3,$ the expression above is equivalent to:
\begin{array}{l}\require{cancel}
3b
.\end{array}
