Precalculus Examples

$(\log_{a} (q) - \log_{a} (r)) + 4 \log_{a} (p)$

Step 1

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

$\log_{a} (\frac{q}{r}) + 4 \log_{a} (p)$

Step 2

Simplify $4 \log_{a} (p)$ by moving $4$ inside the logarithm.

$\log_{a} (\frac{q}{r}) + \log_{a} (p^{4})$

Step 3

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

$\log_{a} (\frac{q}{r} p^{4})$

Step 4

Combine $\frac{q}{r}$ and $p^{4}$ .

$\log_{a} (\frac{q p^{4}}{r})$