Precalculus Examples

$\frac{\log_{5} (9)}{\log_{5} (3)}$

Step 1

Rewrite $\log_{5} (9)$ as $\log_{5} (3^{2})$ .

$\frac{\log_{5} (3^{2})}{\log_{5} (3)}$

Step 2

Expand $\log_{5} (3^{2})$ by moving $2$ outside the logarithm.

$\frac{2 \log_{5} (3)}{\log_{5} (3)}$

Step 3

Cancel the common factor of $\log_{5} (3)$ .

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Cancel the common factor.

$\frac{2 \log_{5} (3)}{\log_{5} (3)}$

Divide $2$ by $1$ .

$2$