Algebra Examples

$\ln (\sqrt{x y})$

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

$\ln ({(x y)}^{\frac{1}{2}})$

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

$\frac{1}{2} \ln (x y)$

Rewrite $\ln (x y)$ as $\ln (x) + \ln (y)$ .

$\frac{1}{2} (\ln (x) + \ln (y))$

Apply the distributive property.

$\frac{1}{2} \ln (x) + \frac{1}{2} \ln (y)$

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

$\frac{\ln (x)}{2} + \frac{1}{2} \ln (y)$

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

$\frac{\ln (x)}{2} + \frac{\ln (y)}{2}$