Simplify/Condense log of 4+3 log of x+ log of y

$\log (4) + 3 \log (x) + \log (y)$

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

$3 \log (x) + \log (4 y)$

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

$\log (x^{3}) + \log (4 y)$

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

$\log (x^{3} (4 y))$

Rewrite using the commutative property of multiplication.

$\log (4 x^{3} y)$