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Core 3 level help

  1. Oct 5, 2007 #1
    Hi.

    Could someone please help me with the following question? I would really appreciate any help as I am totally stuck at the moment.

    ln (2y - 1) = 1 + ln (3 - y)

    Is the answer:

    y = (e + 4) / 3 ?

    Thank you.

    Cathy
     
  2. jcsd
  3. Oct 5, 2007 #2

    Dick

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    Nooo. How did you get that?
     
  4. Oct 5, 2007 #3

    stewartcs

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    Looks like she tried to exponentiate it...which is the incorrect way to solve this problem.
     
  5. Oct 5, 2007 #4

    stewartcs

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    Hint: Use identities...Ln(x/y) = Ln(x) - Ln(y)
     
  6. Oct 5, 2007 #5
    I went to 2y = 1 = e^1 + (3 - y)

    3y = e^1 + 4

    y = e^1 + 4 / 3

    Could someone please tell me where I went wrong?

    Thank you.

    Cathy
     
  7. Oct 5, 2007 #6

    stewartcs

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    Try using the identity that I just posted.
     
  8. Oct 5, 2007 #7

    Dick

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    e^(1+ln(3-y))=e^1*e^(ln(3-y))=e*(3-y). If you exponentiate a sum, it becomes a product.
     
  9. Oct 5, 2007 #8
    Thanks for your help.

    I now have y = (3e + 1) / (e + 2)

    Cathy
     
  10. Oct 5, 2007 #9
    Thank you for your help! :smile:

    Cathy
     
  11. Oct 5, 2007 #10

    stewartcs

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    Which gives...

    Ln(2y - 1) - Ln(3 - y) = 1

    Then using the identity: Ln(x/y) = Ln(x) - Ln(y), gives...

    Ln[(2y - 1)/(3 - y)] = 1

    Can you take it from here?
     
  12. Oct 5, 2007 #11

    stewartcs

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    You're welcome.
     
  13. Oct 6, 2007 #12
    Hi.

    Could someone please help me with this one too?

    Express [(x - 10) / (x - 3)(x + 4)] - [(x - 8) / (x - 3)(2x - 1)] as a single fraction in its simplest form.

    I got up to (3x^3 - 20 x^2 + 93x - 126) / (x - 3)(x + 4)(x - 3)(2x - 1) but do not know whether this is correct or what to do next.

    Any help would be really appreciated.

    Thank you.

    Cathy
     
  14. Oct 7, 2007 #13

    Dick

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    That is correct, but it's unnecessarily complicated. The least common denominator is (x-3)*(x+4)*(2x-1). You don't need the second factor of (x-3).
     
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