Precalculus Examples

$\log_{a} (\frac{x^{3}}{y z^{4}})$

Rewrite $\log_{a} (\frac{x^{3}}{y z^{4}})$ as $\log_{a} (x^{3}) - \log_{a} (y z^{4})$ .

$\log_{a} (x^{3}) - \log_{a} (y z^{4})$

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

$3 \log_{a} (x) - \log_{a} (y z^{4})$

Rewrite $\log_{a} (y z^{4})$ as $\log_{a} (y) + \log_{a} (z^{4})$ .

$3 \log_{a} (x) - (\log_{a} (y) + \log_{a} (z^{4}))$

Expand $\log_{a} (z^{4})$ by moving $4$ outside the logarithm.

$3 \log_{a} (x) - (\log_{a} (y) + 4 \log_{a} (z))$

Simplify each term.

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Apply the distributive property.

$3 \log_{a} (x) - \log_{a} (y) - (4 \log_{a} (z))$

Multiply $4$ by $- 1$ .

$3 \log_{a} (x) - \log_{a} (y) - 4 \log_{a} (z)$