Write as a Single Logarithm 2 log of x+3 log of y

$2 \log (x) + 3 \log (y)$

Simplify each term.

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

$\log (x^{2}) + 3 \log (y)$

Simplify $3 \log (y)$ by moving $3$ inside the logarithm.

$\log (x^{2}) + \log (y^{3})$

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

$\log (x^{2} y^{3})$