Precalculus Examples

$8 \ln (x) - \frac{1}{4} \ln (y)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (x^{8}) - \frac{1}{4} \cdot \ln (y)$

Step 1.2

Multiply $- \frac{1}{4} \ln (y)$ .

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Step 1.2.1

Reorder $\ln (y)$ and $\frac{1}{4}$ .

$\ln (x^{8}) - (\frac{1}{4} \ln (y))$

Step 1.2.2

Simplify $\frac{1}{4} \ln (y)$ by moving $\frac{1}{4}$ inside the logarithm.

$\ln (x^{8}) - \ln (y^{\frac{1}{4}})$

Step 2

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

$\ln (\frac{x^{8}}{y^{\frac{1}{4}}})$