Expand the Logarithmic Expression log base 2 of ( square root of x)/8

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

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

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

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

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

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

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

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

$\frac{1}{2} \log_{2} (x) - 1 \cdot 3$

Multiply $- 1$ by $3$ .

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

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

$\frac{\log_{2} (x)}{2} - 3$