Precalculus Examples

$3 \log (x + y) + 2 \log (x - y) - \log (x^{2} + y^{2})$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log (x + y)$ by moving $3$ inside the logarithm.

$\log ({(x + y)}^{3}) + 2 \log (x - y) - \log (x^{2} + y^{2})$

Step 1.2

Simplify $2 \log (x - y)$ by moving $2$ inside the logarithm.

$\log ({(x + y)}^{3}) + \log ({(x - y)}^{2}) - \log (x^{2} + y^{2})$

Step 2

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

$\log ({(x + y)}^{3} {(x - y)}^{2}) - \log (x^{2} + y^{2})$

Step 3

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

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