Expand the Logarithmic Expression log base 7 of 1/( square root of 7)

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

Rewrite $\log_{7} (\frac{1}{\sqrt{7}})$ as $\log_{7} (1) - \log_{7} (\sqrt{7})$ .

$\log_{7} (1) - \log_{7} (\sqrt{7})$

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

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

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

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

Logarithm base $7$ of $1$ is $0$ .

$0 - (\frac{1}{2} \log_{7} (7))$

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

$0 - (\frac{1}{2} \cdot 1)$

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

$0 - \frac{1}{2}$

Subtract $\frac{1}{2}$ from $0$ .

$- \frac{1}{2}$