Precalculus Examples

$\frac{3}{2} \cdot \log_{2} (x - y) - 2 \log_{2} (3 x + 7)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{3}{2} \log_{2} (x - y)$ by moving $\frac{3}{2}$ inside the logarithm.

$\log_{2} ({(x - y)}^{\frac{3}{2}}) - 2 \log_{2} (3 x + 7)$

Step 1.2

Simplify $- 2 \log_{2} (3 x + 7)$ by moving $2$ inside the logarithm.

$\log_{2} ({(x - y)}^{\frac{3}{2}}) - \log_{2} ({(3 x + 7)}^{2})$

Step 2

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

$\log_{2} (\frac{{(x - y)}^{\frac{3}{2}}}{{(3 x + 7)}^{2}})$