Precalculus Examples

$3 \ln (5) - \frac{1}{2} \cdot \ln (x^{2} + 4)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \ln (5)$ by moving $3$ inside the logarithm.

$\ln (5^{3}) - \frac{1}{2} \cdot \ln (x^{2} + 4)$

Step 1.2

Raise $5$ to the power of $3$ .

$\ln (125) - \frac{1}{2} \cdot \ln (x^{2} + 4)$

Step 1.3

Multiply $- \frac{1}{2} \ln (x^{2} + 4)$ .

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Step 1.3.1

Reorder $\ln (x^{2} + 4)$ and $\frac{1}{2}$ .

$\ln (125) - (\frac{1}{2} \ln (x^{2} + 4))$

Step 1.3.2

Simplify $\frac{1}{2} \ln (x^{2} + 4)$ by moving $\frac{1}{2}$ inside the logarithm.

$\ln (125) - \ln ({(x^{2} + 4)}^{\frac{1}{2}})$

Step 2

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

$\ln (\frac{125}{{(x^{2} + 4)}^{\frac{1}{2}}})$