Precalculus Examples

$4 \ln (6) + 5 \ln (x) + 5 \ln (x^{2} + 6)$

Step 1

Simplify each term.

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Step 1.1

Simplify $4 \ln (6)$ by moving $4$ inside the logarithm.

$\ln (6^{4}) + 5 \ln (x) + 5 \ln (x^{2} + 6)$

Step 1.2

Raise $6$ to the power of $4$ .

$\ln (1296) + 5 \ln (x) + 5 \ln (x^{2} + 6)$

Step 1.3

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

$\ln (1296) + \ln (x^{5}) + 5 \ln (x^{2} + 6)$

Step 1.4

Simplify $5 \ln (x^{2} + 6)$ by moving $5$ inside the logarithm.

$\ln (1296) + \ln (x^{5}) + \ln ({(x^{2} + 6)}^{5})$

Step 2

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

$\ln (1296 x^{5}) + \ln ({(x^{2} + 6)}^{5})$

Step 3

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

$\ln (1296 x^{5} {(x^{2} + 6)}^{5})$