Precalculus Examples

$\log_{7} (\frac{a^{7}}{b^{6} c})$

Step 1

Rewrite $\log_{7} (\frac{a^{7}}{b^{6} c})$ as $\log_{7} (a^{7}) - \log_{7} (b^{6} c)$ .

$\log_{7} (a^{7}) - \log_{7} (b^{6} c)$

Step 2

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

$7 \log_{7} (a) - \log_{7} (b^{6} c)$

Step 3

Rewrite $\log_{7} (b^{6} c)$ as $\log_{7} (b^{6}) + \log_{7} (c)$ .

$7 \log_{7} (a) - (\log_{7} (b^{6}) + \log_{7} (c))$

Step 4

Expand $\log_{7} (b^{6})$ by moving $6$ outside the logarithm.

$7 \log_{7} (a) - (6 \log_{7} (b) + \log_{7} (c))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$7 \log_{7} (a) - (6 \log_{7} (b)) - \log_{7} (c)$

Step 5.2

Multiply $6$ by $- 1$ .

$7 \log_{7} (a) - 6 \log_{7} (b) - \log_{7} (c)$