Expand the Logarithmic Expression log of square root of 100z

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

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

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

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

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

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

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

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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