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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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