Simplify/Condense 8 natural log of x+9-4 natural log of x

$8 \ln (x + 9) - 4 \ln (x)$

Step 1

Simplify each term.

Simplify $8 \ln (x + 9)$ by moving $8$ inside the logarithm.

$\ln ({(x + 9)}^{8}) - 4 \ln (x)$

Simplify $- 4 \ln (x)$ by moving $4$ inside the logarithm.

$\ln ({(x + 9)}^{8}) - \ln (x^{4})$

Step 2

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

$\ln (\frac{{(x + 9)}^{8}}{x^{4}})$