SOLUTION: ln{[(𝑥^15)(x-1)^1/2]/(3x-16)}=𝐴ln𝑥+𝐵ln(𝑥−1)+𝐶ln(3𝑥−16) 1)with the constant A=? 2)the constant B=? 3)and the constant C=?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: ln{[(𝑥^15)(x-1)^1/2]/(3x-16)}=𝐴ln𝑥+𝐵ln(𝑥−1)+𝐶ln(3𝑥−16) 1)with the constant A=? 2)the constant B=? 3)and the constant C=?      Log On


   

Question 1164820: ln{[(𝑥^15)(x-1)^1/2]/(3x-16)}=𝐴ln𝑥+𝐵ln(𝑥−1)+𝐶ln(3𝑥−16)
1)with the constant A=?
2)the constant B=?
3)and the constant C=?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
given:


ln%28%28x%5E15%28x-1%29%5E%281%2F2%29%29%2F%283x-16%29%29

=ln%28x%5E15%28x-1%29%5E%281%2F2%29%29-ln%283x-16%29

=ln%28x%5E15%29%2Bln%28%28x-1%29%5E%281%2F2%29%29-ln%283x-16%29

=15ln%28x%29%2B%281%2F2%29ln%28x-1%29-ln%283x-16%29
so, A=15, B=1%2F2, and C=1

and


Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!
ln{[(𝑥^15)(x-1)^1/2]/(3x-16)}=𝐴ln𝑥+𝐵ln(𝑥−1)+𝐶ln(3𝑥−16)

1)with the constant A=?
2)the constant B=?
3)and the constant C=?



 = Aln(x) + Bln(x - 1) + Cln(3x - 16)

 = Aln(x) + Bln(x - 1) + Cln(3x - 16)

15ln%28x%29+%2B+%281%2F2%29ln%28x+-+1%29+-+ln%283x+-+16%29 = Aln(x) + Bln(x - 1) + Cln(3x - 16)

 15ln(x) + highlight_green%281%2F2%29ln(x - 1) - 1ln(3x - 16)
 
  Aln(x) +  Bln(x - 1) + Cln(3x - 16)


Comparing coefficients above, we see that