Precalculus Examples

$4 \log (x) + \log (y) - \log (z)$

Step 1

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

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

Step 2

Simplify $4 \log (x)$ by moving $4$ inside the logarithm.

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

Step 3

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

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

Step 4

Combine $x^{4}$ and $\frac{y}{z}$ .

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