Precalculus Examples

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

Step 1

Rewrite $\log_{3} (9 \sqrt{b})$ as $\log_{3} (9) + \log_{3} (\sqrt{b})$ .

$\log_{3} (9) + \log_{3} (\sqrt{b})$

Step 2

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

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

Step 3

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

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

Step 4

Logarithm base $3$ of $9$ is $2$ .

$2 + \frac{1}{2} \log_{3} (b)$

Step 5

Combine $\frac{1}{2}$ and $\log_{3} (b)$ .

$2 + \frac{\log_{3} (b)}{2}$