Precalculus Examples

$\log (x \sqrt{z})$

Step 1

Rewrite $\log (x \sqrt{z})$ as $\log (x) + \log (\sqrt{z})$ .

$\log (x) + \log (\sqrt{z})$

Step 2

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

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

Step 3

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

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

Step 4

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

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