What is ln(x^2-5x+6)-ln(x^2-4)+ln(x+2) ?

The solution to ln(x^2-5x+6)-ln(x^2-4)+ln(x+2) is ln(x-3)

Popular >

simplify ln(x^2-5x+6)-ln(x^2-4)+ln(x+2)

simplify

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

ln (x - 3)

Solution steps

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{2} - 5 x + 6) - ln (x^{2} - 4) = ln (\frac{x ^{2} - 5 x + 6}{x ^{2} - 4})

= ln (\frac{x ^{2} - 5 x + 6}{x ^{2} - 4}) + ln (x + 2)

Simplify

\frac{x ^{2} - 5 x + 6}{x ^{2} - 4} : \frac{x - 3}{x + 2}

= ln (\frac{x - 3}{x + 2}) + ln (x + 2)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{x - 3}{x + 2}) + ln (x + 2) = ln (\frac{x - 3}{x + 2} (x + 2))

= ln (\frac{x - 3}{x + 2} (x + 2))

Simplify

\frac{x - 3}{x + 2} (x + 2) : x - 3

= ln (x - 3)

lo g_{2} (9) - lo g_{2} (y) + \frac{1}{2} lo g_{2} (x) - lo g_{2} (3)

3 ln (x) - \frac{3}{2} ln (y) + 4 ln (z)

ln (\frac{2 ^{2}}{3 ^{3} 5 ^{4}})

ln (\frac{x x - 9}{x ^{5} + 9})

What is ln(x^2-5x+6)-ln(x^2-4)+ln(x+2) ?
The solution to ln(x^2-5x+6)-ln(x^2-4)+ln(x+2) is ln(x-3)