Expand the Logarithmic Expression log base 2 of square root of 4x

$\log_{2} (\sqrt{4 x})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x}$ as ${(4 x)}^{\frac{1}{2}}$ .

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

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

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

Rewrite $\log_{2} (4 x)$ as $\log_{2} (4) + \log_{2} (x)$ .

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

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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