Precalculus Examples

$\frac{\ln (3) + 2 \ln (x)}{8 \ln (y)}$

Step 1

Simplify the numerator.

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Step 1.1

Simplify $2 \ln (x)$ by moving $2$ inside the logarithm.

$\frac{\ln (3) + \ln (x^{2})}{8 \ln (y)}$

Step 1.2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\ln (3 x^{2})}{8 \ln (y)}$

Step 2

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

$\frac{\ln (3 x^{2})}{\ln (y^{8})}$