Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify $\frac{1}{2} \log_{6} (x + \log_{6} (\frac{y}{{(x + 3)}^{6}}))$ by moving $\frac{1}{2}$ inside the logarithm.

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