Precalculus Examples

$\ln (2 x - 1) - 5 \ln (x + 1) - 4 \ln (x + 2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $- 5 \ln (x + 1)$ by moving $5$ inside the logarithm.

$\ln (2 x - 1) - \ln ({(x + 1)}^{5}) - 4 \ln (x + 2)$

Step 1.2

Simplify $- 4 \ln (x + 2)$ by moving $4$ inside the logarithm.

$\ln (2 x - 1) - \ln ({(x + 1)}^{5}) - \ln ({(x + 2)}^{4})$

Step 2

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

$\ln (\frac{2 x - 1}{{(x + 1)}^{5}}) - \ln ({(x + 2)}^{4})$

Step 3

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

$\ln (\frac{\frac{2 x - 1}{{(x + 1)}^{5}}}{{(x + 2)}^{4}})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\ln (\frac{2 x - 1}{{(x + 1)}^{5}} \cdot \frac{1}{{(x + 2)}^{4}})$

Step 5

Multiply $\frac{2 x - 1}{{(x + 1)}^{5}}$ by $\frac{1}{{(x + 2)}^{4}}$ .

$\ln (\frac{2 x - 1}{{(x + 1)}^{5} {(x + 2)}^{4}})$