Precalculus Examples

$\ln (5) + 2 \ln (x) + 3 \ln (x^{2} + 5)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (5) + \ln (x^{2}) + 3 \ln (x^{2} + 5)$

Step 1.2

Simplify $3 \ln (x^{2} + 5)$ by moving $3$ inside the logarithm.

$\ln (5) + \ln (x^{2}) + \ln ({(x^{2} + 5)}^{3})$

Step 2

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

$\ln (5 x^{2}) + \ln ({(x^{2} + 5)}^{3})$

Step 3

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

$\ln (5 x^{2} {(x^{2} + 5)}^{3})$