Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Rewrite $\log (x^{2} y)$ as $\log (x^{2}) + \log (y)$ .

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

Step 6

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

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