Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Logarithm base $a$ of $a$ is $1$ .

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

Step 5

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

$k \frac{1}{2}$

Step 6

Combine $k$ and $\frac{1}{2}$ .

$\frac{k}{2}$