Write as a Single Logarithm log of 4- log of z+4 log of y

$\log (4) - \log (z) + 4 \log (y)$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{4}{z}) + 4 \log (y)$

Simplify $4 \log (y)$ by moving $4$ inside the logarithm.

$\log (\frac{4}{z}) + \log (y^{4})$

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

$\log (\frac{4}{z} y^{4})$

Combine $\frac{4}{z}$ and $y^{4}$ .

$\log (\frac{4 y^{4}}{z})$