Precalculus Examples

$9 \ln (x - 3) - 11 \ln (x)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $9 \ln (x - 3)$ by moving $9$ inside the logarithm.

$\ln ({(x - 3)}^{9}) - 11 \ln (x)$

Step 1.2

Simplify $- 11 \ln (x)$ by moving $11$ inside the logarithm.

$\ln ({(x - 3)}^{9}) - \ln (x^{11})$

Step 2

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

$\ln (\frac{{(x - 3)}^{9}}{x^{11}})$