Simplify/Condense log of x^2-5x+6- log of x-2

$\log (x^{2} - 5 x + 6) - \log (x - 2)$

Step 1

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

$\log (\frac{x^{2} - 5 x + 6}{x - 2})$

Step 2

Factor $x^{2} - 5 x + 6$ 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 $6$ and whose sum is $- 5$ .

$- 3, - 2$

Write the factored form using these integers.

$\log (\frac{(x - 3) (x - 2)}{x - 2})$

Step 3

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\log (\frac{(x - 3) (x - 2)}{x - 2})$

Divide $x - 3$ by $1$ .

$\log (x - 3)$

Simplify/Condense log of x^2-5x+6- log of x-2

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