Precalculus Examples

$\frac{\log (8)}{\log (6)}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\log (2^{3})}{\log (6)}$

Step 1.2

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

$\frac{3 \log (2)}{\log (6)}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\log (6)$ as $\log (2 (3))$ .

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

Step 2.2

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$\frac{3 \log (2)}{\log (2) + \log (3)}$