Trigonometry Examples

$\ln (\sqrt[5]{6})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{6}$ as $6^{\frac{1}{5}}$ .

$\ln (6^{\frac{1}{5}})$

Step 2

Expand $\ln (6^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\frac{1}{5} \ln (6)$

Step 3

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

$\frac{1}{5} \ln (2 (3))$

Step 4

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

$\frac{1}{5} (\ln (2) + \ln (3))$

Step 5

Apply the distributive property.

$\frac{1}{5} \ln (2) + \frac{1}{5} \ln (3)$

Step 6

Combine $\frac{1}{5}$ and $\ln (2)$ .

$\frac{\ln (2)}{5} + \frac{1}{5} \ln (3)$

Step 7

Combine $\frac{1}{5}$ and $\ln (3)$ .

$\frac{\ln (2)}{5} + \frac{\ln (3)}{5}$