Precalculus Examples

$\log (3) + 2 \log (x) - 5 \log (y)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (3) + \log (x^{2}) - 5 \log (y)$

Step 1.2

Simplify $- 5 \log (y)$ by moving $5$ inside the logarithm.

$\log (3) + \log (x^{2}) - \log (y^{5})$

Step 2

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

$\log (3 x^{2}) - \log (y^{5})$

Step 3

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

$\log (\frac{3 x^{2}}{y^{5}})$