Precalculus Examples

$6 \ln (x) + 2 \ln (y) - 4 \ln (2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $6 \ln (x)$ by moving $6$ inside the logarithm.

$\ln (x^{6}) + 2 \ln (y) - 4 \ln (2)$

Step 1.2

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

$\ln (x^{6}) + \ln (y^{2}) - 4 \ln (2)$

Step 1.3

Simplify $- 4 \ln (2)$ by moving $4$ inside the logarithm.

$\ln (x^{6}) + \ln (y^{2}) - \ln (2^{4})$

Step 1.4

Raise $2$ to the power of $4$ .

$\ln (x^{6}) + \ln (y^{2}) - \ln (16)$

Step 2

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

$\ln (x^{6} y^{2}) - \ln (16)$

Step 3

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

$\ln (\frac{x^{6} y^{2}}{16})$