Precalculus Examples

$\frac{\log (9)}{\log (4)}$

Step 1

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

$\frac{\log (3^{2})}{\log (4)}$

Step 2

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

$\frac{2 \log (3)}{\log (4)}$

Step 3

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

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

Step 4

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

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

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.58496250 \dots$