Precalculus Examples

$3 \ln (x) (2 \ln (y) - 4 \ln (x + 1)) + 3 \ln (y)$

Step 1

Simplify $3 \ln (x)$ by moving $3$ inside the logarithm.

$\ln (x^{3}) (2 \ln (y) - 4 \ln (x + 1)) + 3 \ln (y)$

Step 2

Simplify each term.

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Step 2.1

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

$\ln (x^{3}) (\ln (y^{2}) - 4 \ln (x + 1)) + 3 \ln (y)$

Step 2.2

Simplify $- 4 \ln (x + 1)$ by moving $4$ inside the logarithm.

$\ln (x^{3}) (\ln (y^{2}) - \ln ({(x + 1)}^{4})) + 3 \ln (y)$

Step 3

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

$\ln (x^{3}) \ln (\frac{y^{2}}{{(x + 1)}^{4}}) + 3 \ln (y)$

Step 4

Simplify $3 \ln (y)$ by moving $3$ inside the logarithm.

$\ln (x^{3}) \ln (\frac{y^{2}}{{(x + 1)}^{4}}) + \ln (y^{3})$