Precalculus Examples

$\ln (a + b) + 3 \ln (a - b) - 5 \ln (c)$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \ln (a - b)$ by moving $3$ inside the logarithm.

$\ln (a + b) + \ln ({(a - b)}^{3}) - 5 \ln (c)$

Step 1.2

Simplify $- 5 \ln (c)$ by moving $5$ inside the logarithm.

$\ln (a + b) + \ln ({(a - b)}^{3}) - \ln (c^{5})$

Step 2

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

$\ln ((a + b) {(a - b)}^{3}) - \ln (c^{5})$

Step 3

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

$\ln (\frac{(a + b) {(a - b)}^{3}}{c^{5}})$