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Logarithmic equations help

  1. Aug 23, 2008 #1
    3e3y-6 = 2x2-1
    ln3e3y-6=ln2x2-lne
    ln3e3y-6=ln2x2/lne
    3e3y-6=2x2/e
    3e3y-6*e=2x2
    e3y-6=(2/3)x2
    3y-6=ln((2/3)x2)
    3y=ln((2/3)x2)+6
    y=(1/3)ln((2/3)x2)+2

    I wonder the answer is correct, the question is asking about the equation of y.
     
    Last edited: Aug 23, 2008
  2. jcsd
  3. Aug 23, 2008 #2

    HallsofIvy

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    Re: Logarithm

    Be carefule with parentheses: you mean ln3e3y-6=ln(2x2-1) because you are taking the log of the entire right side: 2x2- 1.

    You see? Now you are treating that "-1" as if it were outside the logarithm: it isn't.

    And even if it were, "ln a- ln b" is NOT "ln a/ln b" it is ln(a/b)

    If you reverse what you did in the first step you should just come back to the first step! You don't because you have done it wrong.
    ln(3e3y- 6)= ln(e3y- 6)+ ln 3= 3y- 6+ ln 3
    3y- 6+ ln 3= ln(2x2- 1)

    Solve that for y.

    No, make the corrections I suggested.
     
  4. Aug 23, 2008 #3
    Re: Logarithm

    ln(3e3y- 6)= ln(e3y- 6)+ ln 3= 3y- 6+ ln 3
    3y- 6+ ln 3= ln(2x2- 1)
    3y-6 = ln((2x2-1)/3)
    3y = ln ((2x2-1)/3) + 6
    y=(1/3)ln((2x2-1)/3)+2
     
  5. Aug 23, 2008 #4
    Re: Logarithm

    Yes, that's what I got
     
  6. Aug 23, 2008 #5
    Re: Logarithm

    New Question:

    log8(9y + 14) = 6x6-11
    9y+14 = 86x6-11

    The next step is it by entering this step??
     
  7. Aug 23, 2008 #6
    Re: Logarithm

    If you're solving for y again then yes that is correct as a next step.
     
  8. Aug 23, 2008 #7
    Re: Logarithm

    the next 2 step will be:

    ln 9y + 14 = ln86x6-11
    ln 9y + 14 = 6x6-11 ln8
     
  9. Aug 23, 2008 #8
    Re: Logarithm

    log8(9y + 14) = 6x6-11
    9y+14 = 86x6-11
    ln (9y + 14) = ln86x6-11
    ln (9y + 14) = (6x6-11) ln8
    ln 9y + ln 14 = (6x6-11)ln8
    ln9y=(6x6-11)ln8 - ln 14
    y=((6x6-11)ln8 - ln 14)/ln9

    Solve the equation of y, i wonder if this is right?
     
  10. Aug 23, 2008 #9

    HallsofIvy

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    Re: Logarithm

    This is NOT the equation you gave before! Before it was ln(3e3y- 6)

    And if the "-6" was NOT in the exponent this is wrong. Did you mean "ln(3e3y- 6"?

     
  11. Aug 23, 2008 #10

    tiny-tim

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    Hi fr33pl4gu3!
    No … ln (9y + 14) is not the same as ln 9y + ln 14, is it? :wink:

    btw you should learn the very useful formula lnab = lnb/lna :smile:
     
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