Write as a Single Logarithm 5 log base b of q+2 log base b of y

$5 \log_{b} (q) + 2 \log_{b} (y)$

Simplify each term.

Simplify $5 \log_{b} (q)$ by moving $5$ inside the logarithm.

$\log_{b} (q^{5}) + 2 \log_{b} (y)$

Simplify $2 \log_{b} (y)$ by moving $2$ inside the logarithm.

$\log_{b} (q^{5}) + \log_{b} (y^{2})$

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{b} (q^{5} y^{2})$