Precalculus Examples

$\ln (2) + \ln (11) - 2 \ln (7)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (2 \cdot 11) - 2 \ln (7)$

Step 2

Simplify each term.

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Multiply $2$ by $11$ .

$\ln (22) - 2 \ln (7)$

Simplify $- 2 \ln (7)$ by moving $2$ inside the logarithm.

$\ln (22) - \ln (7^{2})$

Raise $7$ to the power of $2$ .

$\ln (22) - \ln (49)$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{22}{49})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{22}{49})$

Decimal Form:

$- 0.80077784 \dots$