Precalculus Examples

$\log_{4} (x) - \log_{4} (y) + 3 \log_{4} (z)$

Step 1

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

$\log_{4} (\frac{x}{y}) + 3 \log_{4} (z)$

Step 2

Simplify $3 \log_{4} (z)$ by moving $3$ inside the logarithm.

$\log_{4} (\frac{x}{y}) + \log_{4} (z^{3})$

Step 3

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

$\log_{4} (\frac{x}{y} z^{3})$

Step 4

Combine $\frac{x}{y}$ and $z^{3}$ .

$\log_{4} (\frac{x z^{3}}{y})$