Precalculus Examples

$2 \log (x) - (\log (y) - \log (z))$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Combine $x^{2}$ and $\frac{z}{y}$ .

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