Precalculus Examples

$\log (3 \sqrt{2})$

Step 1

Rewrite $\log (3 \sqrt{2})$ as $\log (3) + \log (\sqrt{2})$ .

$\log (3) + \log (\sqrt{2})$

Step 2

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

$\log (3) + \log (2^{\frac{1}{2}})$

Step 3

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

$\log (3) + \frac{1}{2} \log (2)$

Step 4

Combine $\frac{1}{2}$ and $\log (2)$ .

$\log (3) + \frac{\log (2)}{2}$