Precalculus Examples

$\ln (12) + 5 \ln (x) - 8 \ln (y)$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \ln (x)$ by moving $5$ inside the logarithm.

$\ln (12) + \ln (x^{5}) - 8 \ln (y)$

Step 1.2

Simplify $- 8 \ln (y)$ by moving $8$ inside the logarithm.

$\ln (12) + \ln (x^{5}) - \ln (y^{8})$

Step 2

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

$\ln (12 x^{5}) - \ln (y^{8})$

Step 3

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

$\ln (\frac{12 x^{5}}{y^{8}})$