Precalculus Examples

$\log_{q} (\sqrt[5]{q})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{q}$ as $q^{\frac{1}{5}}$ .

$\log_{q} (q^{\frac{1}{5}})$

Step 2

Expand $\log_{q} (q^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\frac{1}{5} \log_{q} (q)$

Step 3

Logarithm base $q$ of $q$ is $1$ .

$\frac{1}{5} \cdot 1$

Step 4

Multiply $\frac{1}{5}$ by $1$ .

$\frac{1}{5}$