Precalculus Examples

$2 \log_{4} (x) - \log_{4} (y) - \log_{4} (z)$

Step 1

Simplify $2 \log_{4} (x)$ by moving $2$ inside the logarithm.

$\log_{4} (x^{2}) - \log_{4} (y) - \log_{4} (z)$

Step 2

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

$\log_{4} (\frac{x^{2}}{y}) - \log_{4} (z)$

Step 3

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

$\log_{4} (\frac{\frac{x^{2}}{y}}{z})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{4} (\frac{x^{2}}{y} \cdot \frac{1}{z})$

Step 5

Combine.

$\log_{4} (\frac{x^{2} \cdot 1}{y z})$

Step 6

Multiply $x^{2}$ by $1$ .

$\log_{4} (\frac{x^{2}}{y z})$