Precalculus Examples

$(\log_{a} (x) - \log_{a} (y)) + 6 \log_{a} (z)$

Step 1

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

$\log_{a} (\frac{x}{y}) + 6 \log_{a} (z)$

Step 2

Simplify $6 \log_{a} (z)$ by moving $6$ inside the logarithm.

$\log_{a} (\frac{x}{y}) + \log_{a} (z^{6})$

Step 3

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

$\log_{a} (\frac{x}{y} z^{6})$

Step 4

Combine $\frac{x}{y}$ and $z^{6}$ .

$\log_{a} (\frac{x z^{6}}{y})$