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