Write as a Single Logarithm 5 log of x+6 log of x+7

$5 \log (x) + 6 \log (x + 7)$

Step 1

Simplify each term.

Simplify $5 \log (x)$ by moving $5$ inside the logarithm.

$\log (x^{5}) + 6 \log (x + 7)$

Simplify $6 \log (x + 7)$ by moving $6$ inside the logarithm.

$\log (x^{5}) + \log ({(x + 7)}^{6})$

Step 2

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

$\log (x^{5} {(x + 7)}^{6})$