Precalculus Examples

$3 \log_{3} (x) - \log_{3} (\frac{1}{y})$

Step 1

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

$\log_{3} (x^{3}) - \log_{3} (\frac{1}{y})$

Step 2

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

$\log_{3} (\frac{x^{3}}{\frac{1}{y}})$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\log_{3} (x^{3} y)$