Precalculus Examples

$\ln (10) + 4 \ln (x) + 4 \ln (x^{2} + 10)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (10) + \ln (x^{4}) + 4 \ln (x^{2} + 10)$

Step 1.2

Simplify $4 \ln (x^{2} + 10)$ by moving $4$ inside the logarithm.

$\ln (10) + \ln (x^{4}) + \ln ({(x^{2} + 10)}^{4})$

Step 2

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

$\ln (10 x^{4}) + \ln ({(x^{2} + 10)}^{4})$

Step 3

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

$\ln (10 x^{4} {(x^{2} + 10)}^{4})$