Precalculus Examples

$\ln (x) - \frac{1}{3} \cdot \ln (x^{2} - 3)$

Step 1

Multiply $- \frac{1}{3} \ln (x^{2} - 3)$ .

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Step 1.1

Reorder $\ln (x^{2} - 3)$ and $\frac{1}{3}$ .

$\ln (x) - (\frac{1}{3} \ln (x^{2} - 3))$

Step 1.2

Simplify $\frac{1}{3} \ln (x^{2} - 3)$ by moving $\frac{1}{3}$ inside the logarithm.

$\ln (x) - \ln ({(x^{2} - 3)}^{\frac{1}{3}})$

Step 2

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

$\ln (\frac{x}{{(x^{2} - 3)}^{\frac{1}{3}}})$