Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Logarithm base $f$ of $f$ is $1$ .

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

Step 5

Multiply $- 1$ by $1$ .

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

Step 6

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

$0 - 1$

Step 7

Subtract $1$ from $0$ .

$- 1$