Precalculus Examples

$\log_{3} (x) + \log_{3} (y) - 2 \log_{3} (r)$

Step 1

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

$\log_{3} (x y) - 2 \log_{3} (r)$

Step 2

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

$\log_{3} (x y) - \log_{3} (r^{2})$

Step 3

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

$\log_{3} (\frac{x y}{r^{2}})$