Write as a Single Logarithm natural log of x^2+18x+80- natural log of x+8

$\ln (x^{2} + 18 x + 80) - \ln (x + 8)$

Step 1

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

$\ln (\frac{x^{2} + 18 x + 80}{x + 8})$

Step 2

Factor $x^{2} + 18 x + 80$ using the AC method.

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 $80$ and whose sum is $18$ .

$8, 10$

Write the factored form using these integers.

$\ln (\frac{(x + 8) (x + 10)}{x + 8})$

Step 3

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\ln (\frac{(x + 8) (x + 10)}{x + 8})$

Divide $x + 10$ by $1$ .

$\ln (x + 10)$

Write as a Single Logarithm natural log of x^2+18x+80- natural log of x+8

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