Precalculus Examples

$\log_{7} (\frac{32}{5})$

Step 1

Rewrite $\log_{7} (\frac{32}{5})$ as $\log_{7} (32) - \log_{7} (5)$ .

$\log_{7} (32) - \log_{7} (5)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{7} (32)$ as $\log_{7} (2^{5})$ .

$\log_{7} (2^{5}) - \log_{7} (5)$

Step 2.2

Expand $\log_{7} (2^{5})$ by moving $5$ outside the logarithm.

$5 \log_{7} (2) - \log_{7} (5)$