Precalculus Examples

$\log_{6} (z^{2} \sqrt{x})$

Step 1

Rewrite $\log_{6} (z^{2} \sqrt{x})$ as $\log_{6} (z^{2}) + \log_{6} (\sqrt{x})$ .

$\log_{6} (z^{2}) + \log_{6} (\sqrt{x})$

Step 2

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

$\log_{6} (z^{2}) + \log_{6} (x^{\frac{1}{2}})$

Step 3

Expand $\log_{6} (z^{2})$ by moving $2$ outside the logarithm.

$2 \log_{6} (z) + \log_{6} (x^{\frac{1}{2}})$

Step 4

Expand $\log_{6} (x^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$2 \log_{6} (z) + \frac{1}{2} \log_{6} (x)$

Step 5

Combine $\frac{1}{2}$ and $\log_{6} (x)$ .

$2 \log_{6} (z) + \frac{\log_{6} (x)}{2}$