Answer
$\$300,000$
Work Step by Step
Using the given formula, $
S(x)=100\log_2(x+2)
$, with $x=6$, then
\begin{align*}\require{cancel}
S(6)&=100\log_2(6+2)
\\
&=100\log_28
\\
&=100\log_2 2^3
\\
&=100\cdot3\log_2 2
&(\text{use }\log_b x^y=y\log_b x)
\\
&=100\cdot3(1)
&(\text{use }\log_b b=1)
\\
&=300
.\end{align*}
Hence, the total sales after $6$ weeks, $S(6)$, of introducing a major advertising campaign is $\$300,000$.
