Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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