Algebra Examples

$\ln (x^{2} + 6 x + 8) - \ln (x + 2)$

Step 1

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

$\ln (\frac{x^{2} + 6 x + 8}{x + 2})$

Step 2

Factor $x^{2} + 6 x + 8$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $8$ and whose sum is $6$ .

$2, 4$

Step 2.2

Write the factored form using these integers.

$\ln (\frac{(x + 2) (x + 4)}{x + 2})$

Step 3

Cancel the common factor of $x + 2$ .

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Step 3.1

Cancel the common factor.

$\ln (\frac{(x + 2) (x + 4)}{x + 2})$

Step 3.2

Divide $x + 4$ by $1$ .

$\ln (x + 4)$