Evaluate log base a of 1/a

$\log_{a} (\frac{1}{a})$

Rewrite $\frac{1}{a}$ as $1 a^{- 1}$ .

$\log_{a} (1 a^{- 1})$

Rewrite $\log_{a} (1 a^{- 1})$ as $\log_{a} (1) + \log_{a} (a^{- 1})$ .

$\log_{a} (1) + \log_{a} (a^{- 1})$

Use logarithm rules to move $- 1$ out of the exponent.

$\log_{a} (1) - \log_{a} (a)$

Logarithm base $a$ of $a$ is $1$ .

$\log_{a} (1) - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$\log_{a} (1) - 1$

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

$0 - 1$

Subtract $1$ from $0$ .

$- 1$

Evaluate log base a of 1/a

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