Precalculus Examples

$\log_{4} (\frac{\sqrt{x}}{16})$

Step 1

Rewrite $\log_{4} (\frac{\sqrt{x}}{16})$ as $\log_{4} (\sqrt{x}) - \log_{4} (16)$ .

$\log_{4} (\sqrt{x}) - \log_{4} (16)$

Step 2

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

$\log_{4} (x^{\frac{1}{2}}) - \log_{4} (16)$

Step 3

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

$\frac{1}{2} \log_{4} (x) - \log_{4} (16)$

Step 4

Logarithm base $4$ of $16$ is $2$ .

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

Step 5

Multiply $- 1$ by $2$ .

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

Step 6

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

$\frac{\log_{4} (x)}{2} - 2$