Answer
$n= 3$
Work Step by Step
Given \begin{equation}
40(0.8)^n=20.48.
\end{equation} The is an exponential equation with a base of $b= 0.8$ and an exponent of $n$. We solve it: \begin{equation}
\begin{aligned}
40(0.8)^n&=20.48\\\
(0.8)^n & =\frac{20.48}{40}\\
(0.8)^n& =0.512 \\
\ln\left( 0.8^n \right)& =0.512 \\
n\log\left ( 0.8 \right) & =\log (0.512)\\
n& = \frac{\log (0.512)}{\log\left( 0.8 \right)}\\
n&= 3.
\end{aligned}
\end{equation}
