Algebra Examples

$\ln (\sqrt{a b})$

Step 1

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

$\ln ({(a b)}^{\frac{1}{2}})$

Step 2

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

$\frac{1}{2} \ln (a b)$

Step 3

Rewrite $\ln (a b)$ as $\ln (a) + \ln (b)$ .

$\frac{1}{2} (\ln (a) + \ln (b))$

Step 4

Apply the distributive property.

$\frac{1}{2} \ln (a) + \frac{1}{2} \ln (b)$

Step 5

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

$\frac{\ln (a)}{2} + \frac{1}{2} \ln (b)$

Step 6

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

$\frac{\ln (a)}{2} + \frac{\ln (b)}{2}$