Precalculus Examples

$\ln (a) + \ln (2 y) - 2 \ln (z)$

Step 1

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

$\ln (a (2 y)) - 2 \ln (z)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\ln (2 a y) - 2 \ln (z)$

Step 2.2

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

$\ln (2 a y) - \ln (z^{2})$

Step 3

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

$\ln (\frac{2 a y}{z^{2}})$