Expand the Logarithmic Expression log base 7 of square root of 7

$\log_{7} (\sqrt{7})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\log_{7} (7^{\frac{1}{2}})$

Step 2

Expand $\log_{7} (7^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{7} (7)$

Step 3

Logarithm base $7$ of $7$ is $1$ .

$\frac{1}{2} \cdot 1$

Step 4

Multiply $\frac{1}{2}$ by $1$ .

$\frac{1}{2}$