Precalculus Examples

$\log_{a} (m) - \log_{a} (n) + 3 \log_{a} (k)$

Step 1

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

$\log_{a} (\frac{m}{n}) + 3 \log_{a} (k)$

Step 2

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

$\log_{a} (\frac{m}{n}) + \log_{a} (k^{3})$

Step 3

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

$\log_{a} (\frac{m}{n} k^{3})$

Step 4

Combine $\frac{m}{n}$ and $k^{3}$ .

$\log_{a} (\frac{m k^{3}}{n})$