What is simplify-4ln(x-2)+3ln(1-x) ?

The solution to simplify-4ln(x-2)+3ln(1-x) is ln(((1-x)^3)/((x-2)^4))

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simplify-4ln(x-2)+3ln(1-x)

simplify

- 4 ln (x - 2) + 3 ln (1 - x)

ln (\frac{( 1 - x ) ^{3}}{( x - 2 ) ^{4}})

Solution steps

- 4 ln (x - 2) + 3 ln (1 - x)

Apply log rule:

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

4 ln (x - 2) = ln ((x - 2)^{4})

= - ln ((x - 2)^{4}) + 3 ln (- x + 1)

Apply log rule:

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

3 ln (- x + 1) = ln ((- x + 1)^{3})

= - ln ((x - 2)^{4}) + ln ((- x + 1)^{3})

Apply log rule:

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

ln ((1 - x)^{3}) - ln ((x - 2)^{4}) = ln (\frac{( - x + 1 ) ^{3}}{( x - 2 ) ^{4}})

= ln (\frac{( 1 - x ) ^{3}}{( x - 2 ) ^{4}})

2 lo g_{3} (x - y) - 3 lo g_{3} (m)

ln (A) - ln (B)

ln (\frac{a}{b c})

ln (x) + ln (3 y)

ln (32)

What is simplify-4ln(x-2)+3ln(1-x) ?
The solution to simplify-4ln(x-2)+3ln(1-x) is ln(((1-x)^3)/((x-2)^4))