Precalculus Examples

$\frac{\log (16)}{\log (4)}$

Step 1

Rewrite $\log (16)$ as $\log (2^{4})$ .

$\frac{\log (2^{4})}{\log (4)}$

Step 2

Expand $\log (2^{4})$ by moving $4$ outside the logarithm.

$\frac{4 \log (2)}{\log (4)}$

Step 3

Rewrite $\log (4)$ as $\log (2^{2})$ .

$\frac{4 \log (2)}{\log (2^{2})}$

Step 4

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

$\frac{4 \log (2)}{2 \log (2)}$

Step 5

Cancel the common factor of $4$ and $2$ .

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Step 5.1

Factor $2$ out of $4 \log (2)$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$2$