Simplify/Condense log of y+7 log of z

$\log (y) + 7 \log (z)$

Simplify $7 \log (z)$ by moving $7$ inside the logarithm.

$\log (y) + \log (z^{7})$

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

$\log (y z^{7})$