Precalculus Examples

$\log_{k} (\sqrt{k})$

Step 1

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

$\log_{k} (k^{\frac{1}{2}})$

Step 2

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

$\frac{1}{2} \log_{k} (k)$

Step 3

Logarithm base $k$ of $k$ is $1$ .

$\frac{1}{2} \cdot 1$

Step 4

Multiply $\frac{1}{2}$ by $1$ .

$\frac{1}{2}$