Precalculus Examples

$\ln (\sqrt{5} x y)$

Step 1

Rewrite $\ln (\sqrt{5} x y)$ as $\ln (\sqrt{5} x) + \ln (y)$ .

$\ln (\sqrt{5} x) + \ln (y)$

Step 2

Rewrite $\ln (\sqrt{5} x)$ as $\ln (\sqrt{5}) + \ln (x)$ .

$\ln (\sqrt{5}) + \ln (x) + \ln (y)$

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\ln (5^{\frac{1}{2}}) + \ln (x) + \ln (y)$

Step 4

Expand $\ln (5^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

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

Step 5

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

$\frac{\ln (5)}{2} + \ln (x) + \ln (y)$