Precalculus Examples

$\log ({(\sqrt{3})}^{81})$

Step 1

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

$\log ({(3^{\frac{1}{2}})}^{81})$

Step 2

Expand $\log ({(3^{\frac{1}{2}})}^{81})$ by moving $81$ outside the logarithm.

$81 \log (3^{\frac{1}{2}})$

Step 3

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

$81 (\frac{1}{2} \log (3))$

Step 4

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

$81 \frac{\log (3)}{2}$

Step 5

Combine $81$ and $\frac{\log (3)}{2}$ .

$\frac{81 \log (3)}{2}$