Precalculus Examples

$\log_{a} (\frac{x^{8}}{y z^{9}})$

Step 1

Rewrite $\log_{a} (\frac{x^{8}}{y z^{9}})$ as $\log_{a} (x^{8}) - \log_{a} (y z^{9})$ .

$\log_{a} (x^{8}) - \log_{a} (y z^{9})$

Step 2

Expand $\log_{a} (x^{8})$ by moving $8$ outside the logarithm.

$8 \log_{a} (x) - \log_{a} (y z^{9})$

Step 3

Rewrite $\log_{a} (y z^{9})$ as $\log_{a} (y) + \log_{a} (z^{9})$ .

$8 \log_{a} (x) - (\log_{a} (y) + \log_{a} (z^{9}))$

Step 4

Expand $\log_{a} (z^{9})$ by moving $9$ outside the logarithm.

$8 \log_{a} (x) - (\log_{a} (y) + 9 \log_{a} (z))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$8 \log_{a} (x) - \log_{a} (y) - (9 \log_{a} (z))$

Step 5.2

Multiply $9$ by $- 1$ .

$8 \log_{a} (x) - \log_{a} (y) - 9 \log_{a} (z)$