Precalculus Examples

$\ln (6) + 5 \ln (x) + 9 \ln (x^{2} + 9)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (6) + \ln (x^{5}) + 9 \ln (x^{2} + 9)$

Step 1.2

Simplify $9 \ln (x^{2} + 9)$ by moving $9$ inside the logarithm.

$\ln (6) + \ln (x^{5}) + \ln ({(x^{2} + 9)}^{9})$

Step 2

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

$\ln (6 x^{5}) + \ln ({(x^{2} + 9)}^{9})$

Step 3

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

$\ln (6 x^{5} {(x^{2} + 9)}^{9})$