Precalculus Examples

$\log_{2} (\frac{8}{\sqrt{x} + 5})$

Step 1

Rewrite $\log_{2} (\frac{8}{\sqrt{x} + 5})$ as $\log_{2} (8) - \log_{2} (\sqrt{x} + 5)$ .

$\log_{2} (8) - \log_{2} (\sqrt{x} + 5)$

Step 2

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

$\log_{2} (8) - \log_{2} (x^{\frac{1}{2}} + 5)$

Step 3

Logarithm base $2$ of $8$ is $3$ .

$3 - \log_{2} (x^{\frac{1}{2}} + 5)$