Precalculus Examples

$2 \log_{6} (x) - 12 \log_{6} (y)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log_{6} (x)$ by moving $2$ inside the logarithm.

$\log_{6} (x^{2}) - 12 \log_{6} (y)$

Step 1.2

Simplify $- 12 \log_{6} (y)$ by moving $12$ inside the logarithm.

$\log_{6} (x^{2}) - \log_{6} (y^{12})$

Step 2

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

$\log_{6} (\frac{x^{2}}{y^{12}})$