SOLUTION: value of k for which (x-1)isa factor of (x to the power of 3-k)

Question 443180: value of k for which (x-1)isa factor of (x to the power of 3-k)
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
If x-1 is a factor of x^(3-k), then (x-1) = x^(3-k).
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x^(3-k) = (x^3 / x^k)
x-1 = x^3 /x^k
x^(k+1) - x^k = x^3
x^k * x - x^k = x^3
x^k(x-1) = x^3
x^k = x^3/(x-1)
k*ln(x) = ln(x^3)/ln(x-1)
k = ln(x^3) - ln(x-1) - ln(x)
k = 3ln(x) - ln(x-1) - ln(x)
k = 2ln(x) - ln(x-1)
k = ln ( x^2 / x-1)

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