What is 3ln(x-2)-ln(x^2-5x+6)+2ln(x-3) ?

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

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simplify 3ln(x-2)-ln(x^2-5x+6)+2ln(x-3)

simplify

3 ln (x - 2) - ln (x^{2} - 5 x + 6) + 2 ln (x - 3)

ln ((x - 2)^{2} (x - 3))

Solution steps

3 ln (x - 2) - ln (x^{2} - 5 x + 6) + 2 ln (x - 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (x - 2) = ln ((x - 2)^{3})

= ln ((x - 2)^{3}) - ln (x^{2} - 5 x + 6) + 2 ln (x - 3)

Apply log rule:

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

ln ((x - 2)^{3}) - ln (x^{2} - 5 x + 6) = ln (\frac{( x - 2 ) ^{3}}{x ^{2} - 5 x + 6})

= ln (\frac{( x - 2 ) ^{3}}{x ^{2} - 5 x + 6}) + 2 ln (x - 3)

Simplify

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x - 3) = ln ((x - 3)^{2})

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

Apply log rule:

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

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

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

Simplify

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

= ln ((x - 2)^{2} (x - 3))

(2 ln (3) - 2 ln (9)) - (2 ln (2) - 2 ln (7))

lo g_{6} (6 y w z)

ln (2) + ln (4 x - 1)

- ln (x + 1) + ln (x - 1)

ln (x - 3) - ln (- 3 + x)

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