Precalculus Examples

$\frac{1}{2} \log (x) - \log (y) - 2 \log (z)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{2} \log (x)$ by moving $\frac{1}{2}$ inside the logarithm.

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

Step 1.2

Simplify $- 2 \log (z)$ by moving $2$ inside the logarithm.

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Combine.

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

Step 6

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

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