Simplify/Condense 4 natural log of x+6-3 natural log of x

$4 \ln (x + 6) - 3 \ln (x)$

Step 1

Simplify each term.

Simplify $4 \ln (x + 6)$ by moving $4$ inside the logarithm.

$\ln ({(x + 6)}^{4}) - 3 \ln (x)$

Simplify $- 3 \ln (x)$ by moving $3$ inside the logarithm.

$\ln ({(x + 6)}^{4}) - \ln (x^{3})$

Step 2

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

$\ln (\frac{{(x + 6)}^{4}}{x^{3}})$