Precalculus Examples

$\log_{4} (\sqrt{5 x})$

Step 1

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

$\log_{4} ({(5 x)}^{\frac{1}{2}})$

Step 2

Expand $\log_{4} ({(5 x)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{4} (5 x)$

Step 3

Rewrite $\log_{4} (5 x)$ as $\log_{4} (5) + \log_{4} (x)$ .

$\frac{1}{2} (\log_{4} (5) + \log_{4} (x))$

Step 4

Apply the distributive property.

$\frac{1}{2} \log_{4} (5) + \frac{1}{2} \log_{4} (x)$

Step 5

Combine $\frac{1}{2}$ and $\log_{4} (5)$ .

$\frac{\log_{4} (5)}{2} + \frac{1}{2} \log_{4} (x)$

Step 6

Combine $\frac{1}{2}$ and $\log_{4} (x)$ .

$\frac{\log_{4} (5)}{2} + \frac{\log_{4} (x)}{2}$