Precalculus Examples

$\frac{\ln (8)}{\ln (9)}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$\frac{\ln (2^{3})}{\ln (9)}$

Step 1.2

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$\frac{3 \ln (2)}{\ln (9)}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\ln (9)$ as $\ln (3^{2})$ .

$\frac{3 \ln (2)}{\ln (3^{2})}$

Step 2.2

Expand $\ln (3^{2})$ by moving $2$ outside the logarithm.

$\frac{3 \ln (2)}{2 \ln (3)}$