Expand the Logarithmic Expression log of square root of 100x

$\log (\sqrt{100 x})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{100 x}$ as ${(100 x)}^{\frac{1}{2}}$ .

$\log ({(100 x)}^{\frac{1}{2}})$

Expand $\log ({(100 x)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log (100 x)$

Rewrite $\log (100 x)$ as $\log (100) + \log (x)$ .

$\frac{1}{2} (\log (100) + \log (x))$

Logarithm base $10$ of $100$ is $2$ .

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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