Simplify/Condense log of y+8 log of z

$\log (y) + 8 \log (z)$

Simplify $8 \log (z)$ by moving $8$ inside the logarithm.

$\log (y) + \log (z^{8})$

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

$\log (y z^{8})$