Precalculus Examples

$\log_{7} (\frac{11}{7})$

Step 1

Rewrite $\frac{11}{7}$ as $11 \cdot 7^{- 1}$ .

$\log_{7} (11 \cdot 7^{- 1})$

Step 2

Rewrite $\log_{7} (11 \cdot 7^{- 1})$ as $\log_{7} (11) + \log_{7} (7^{- 1})$ .

$\log_{7} (11) + \log_{7} (7^{- 1})$

Step 3

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

$\log_{7} (11) - \log_{7} (7)$

Step 4

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

$\log_{7} (11) - 1 \cdot 1$

Step 5

Multiply $- 1$ by $1$ .

$\log_{7} (11) - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\log_{7} (11) - 1$

Decimal Form:

$0.23227440 \dots$