Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Multiply $- 1$ by $1$ .

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

Step 6

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

$0 - 1$

Step 7

Subtract $1$ from $0$ .

$- 1$