Expand the Logarithmic Expression log base 5 of 2 square root of x

$\log_{5} (2 \sqrt{x})$

Step 1

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

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

Step 2

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

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

Step 3

Expand $\log_{5} (x^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

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

Step 4

Combine $\frac{1}{2}$ and $\log_{5} (x)$ .

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