Precalculus Examples

$\log_{7} (z^{6} \sqrt{x})$

Step 1

Rewrite $\log_{7} (z^{6} \sqrt{x})$ as $\log_{7} (z^{6}) + \log_{7} (\sqrt{x})$ .

$\log_{7} (z^{6}) + \log_{7} (\sqrt{x})$

Step 2

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

$\log_{7} (z^{6}) + \log_{7} (x^{\frac{1}{2}})$

Step 3

Expand $\log_{7} (z^{6})$ by moving $6$ outside the logarithm.

$6 \log_{7} (z) + \log_{7} (x^{\frac{1}{2}})$

Step 4

Expand $\log_{7} (x^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$6 \log_{7} (z) + \frac{1}{2} \log_{7} (x)$

Step 5

Combine $\frac{1}{2}$ and $\log_{7} (x)$ .

$6 \log_{7} (z) + \frac{\log_{7} (x)}{2}$