Precalculus Examples

$3 \log_{a} (2 x + 1) - 2 \log_{a} (2 x - 1) + 2$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log_{a} (2 x + 1)$ by moving $3$ inside the logarithm.

$\log_{a} ({(2 x + 1)}^{3}) - 2 \log_{a} (2 x - 1) + 2$

Step 1.2

Simplify $- 2 \log_{a} (2 x - 1)$ by moving $2$ inside the logarithm.

$\log_{a} ({(2 x + 1)}^{3}) - \log_{a} ({(2 x - 1)}^{2}) + 2$

Step 2

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

$\log_{a} (\frac{{(2 x + 1)}^{3}}{{(2 x - 1)}^{2}}) + 2$