Precalculus Examples

$\log (\frac{x^{2}}{y \sqrt{z}})$

Rewrite $\log (\frac{x^{2}}{y \sqrt{z}})$ as $\log (x^{2}) - \log (y \sqrt{z})$ .

$\log (x^{2}) - \log (y \sqrt{z})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{z}$ as $z^{\frac{1}{2}}$ .

$\log (x^{2}) - \log (y z^{\frac{1}{2}})$

Expand $\log (x^{2})$ by moving $2$ outside the logarithm.

$2 \log (x) - \log (y z^{\frac{1}{2}})$

Rewrite $\log (y z^{\frac{1}{2}})$ as $\log (y) + \log (z^{\frac{1}{2}})$ .

$2 \log (x) - (\log (y) + \log (z^{\frac{1}{2}}))$

Expand $\log (z^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$2 \log (x) - (\log (y) + \frac{1}{2} \log (z))$

Simplify each term.

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Combine $\frac{1}{2}$ and $\log (z)$ .

$2 \log (x) - (\log (y) + \frac{\log (z)}{2})$

Apply the distributive property.

$2 \log (x) - \log (y) - \frac{\log (z)}{2}$