Precalculus Examples

$\log_{7} (c^{4} \sqrt{a})$

Step 1

Rewrite $\log_{7} (c^{4} \sqrt{a})$ as $\log_{7} (c^{4}) + \log_{7} (\sqrt{a})$ .

$\log_{7} (c^{4}) + \log_{7} (\sqrt{a})$

Step 2

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

$\log_{7} (c^{4}) + \log_{7} (a^{\frac{1}{2}})$

Step 3

Expand $\log_{7} (c^{4})$ by moving $4$ outside the logarithm.

$4 \log_{7} (c) + \log_{7} (a^{\frac{1}{2}})$

Step 4

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

$4 \log_{7} (c) + \frac{1}{2} \log_{7} (a)$

Step 5

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

$4 \log_{7} (c) + \frac{\log_{7} (a)}{2}$