Precalculus Examples

$\log_{9} (\sqrt{\frac{3}{3}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{3}{3}}$ as ${(\frac{3}{3})}^{\frac{1}{2}}$ .

$\log_{9} ({(\frac{3}{3})}^{\frac{1}{2}})$

Step 2

Expand $\log_{9} ({(\frac{3}{3})}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{9} (\frac{3}{3})$

Step 3

Divide $3$ by $3$ .

$\frac{1}{2} \log_{9} (1)$

Step 4

Logarithm base $9$ of $1$ is $0$ .

$\frac{1}{2} \cdot 0$

Step 5

Multiply $\frac{1}{2}$ by $0$ .

$0$