Precalculus Examples

$\ln (8) + 2 \ln (x) - 7 \ln (y)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (8) + \ln (x^{2}) - 7 \ln (y)$

Step 1.2

Simplify $- 7 \ln (y)$ by moving $7$ inside the logarithm.

$\ln (8) + \ln (x^{2}) - \ln (y^{7})$

Step 2

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

$\ln (8 x^{2}) - \ln (y^{7})$

Step 3

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

$\ln (\frac{8 x^{2}}{y^{7}})$