Precalculus Examples

$0.25 \log (x) - \log (y) - \log (z^{2})$

Step 1

Simplify $0.25 \log (x)$ by moving $0.25$ inside the logarithm.

$\log (x^{0.25}) - \log (y) - \log (z^{2})$

Step 2

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

$\log (\frac{x^{0.25}}{y}) - \log (z^{2})$

Step 3

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

$\log (\frac{\frac{x^{0.25}}{y}}{z^{2}})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log (\frac{x^{0.25}}{y} \cdot \frac{1}{z^{2}})$

Step 5

Combine.

$\log (\frac{x^{0.25} \cdot 1}{y z^{2}})$

Step 6

Multiply $x^{0.25}$ by $1$ .

$\log (\frac{x^{0.25}}{y z^{2}})$