Expand natural log of square root of x/y

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

Rewrite $\sqrt{\frac{x}{y}}$ as ${(\frac{x}{y})}^{\frac{1}{2}}$ .

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

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

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

Rewrite $\ln (\frac{x}{y})$ 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 $\ln (y)$ .

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

Expand natural log of square root of x/y

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