Precalculus Examples

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

Step 1

Rewrite $\ln (\frac{\sqrt{2}}{x y})$ as $\ln (\sqrt{2}) - \ln (x y)$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Apply the distributive property.

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