Precalculus Examples

$\frac{1}{2} \cdot \log_{6} (x) + \log_{3} (y) - 6 \log_{3} (x + 7)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{2} \log_{6} (x)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{6} (x^{\frac{1}{2}}) + \log_{3} (y) - 6 \log_{3} (x + 7)$

Step 1.2

Simplify $- 6 \log_{3} (x + 7)$ by moving $6$ inside the logarithm.

$\log_{6} (x^{\frac{1}{2}}) + \log_{3} (y) - \log_{3} ({(x + 7)}^{6})$

Step 2

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

$\log_{6} (x^{\frac{1}{2}}) + \log_{3} (\frac{y}{{(x + 7)}^{6}})$