Answer
$3a+2c+1$
Work Step by Step
$72=8\cdot 9=2^{3}\cdot 3^{2}$
$\log_{b}(72b)=\log_{b}(2^{3}\cdot 3^{2}\cdot b)$
... apply $\ \ \log_{a}xy=\log_{a}x+\log_{a}y$
$=\log_{b}2^{3}+\log_{b}3^{2}+\log_{b}b$
... apply $\ \ \log_{a}x^{r}=r\log_{a}x$
... apply $\ \ \log_{b}b=1$
$=3\log_{b}2+2\log_{b}3+1$
$=3a+2c+1$
