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Solve this logarithm

  1. Mar 9, 2015 #1
    • Moved from a technical math section, so missing the template
    I need to solve log3(2x+3)-log3(x-2)=3 where 3 is the base.

    This is my attempt at a solution..
    Log3(2x+3)-log3(x-2)=2
    Log3(x-3/2)=2
    Log3(x) - Log3(-3/2) = 2
    Log3(x)-0.369=2
    log3(x)=2.369

    3^2.369=13.4
    x=13.4

    I plugged that into the original equation and I know it is not correct. Can anyone try to steer me in the right direction?
    Been a while on this log business..
     
  2. jcsd
  3. Mar 9, 2015 #2

    mfb

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    What did you do between those lines?
    The following step is wrong as well.
     
    Last edited: Mar 9, 2015
  4. Mar 9, 2015 #3

    Quantum Defect

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    The difference between two logs is the same thing as the log of the quotient.

    log A - log B = log(A/B)

    https://www.khanacademy.org/math/al...properties/v/sum-of-logarithms-with-same-base

    Also, in the top you have the right hand side equal to "3," but in your work, you have this equal to "2" ...
     
  5. Mar 9, 2015 #4
    Ok, let me try that again.

    Equation is log3(2x+3)-log3(x-2)=2
    log3((2x/x)+(3/-2))=2
    log3(2x-1.5)=2
    log3(2x-1.5)=2
    Into exponential form, 3^2=2x-1.5
    X=3.75

    But I solved that out and it doesnt seem to work either.
     
  6. Mar 9, 2015 #5

    Quantum Defect

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    I get log3[(2x+3)/(x-2)] for the first bit of the l.h.s.
     
  7. Mar 9, 2015 #6
    Which would give you log3(2x-3/2), correct?
     
  8. Mar 9, 2015 #7

    mfb

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    No it would not.

    Okay, here is an important subproblem: simplify (2x+3)/(x-2)
     
  9. Mar 9, 2015 #8

    Mark44

    Staff: Mentor

    The first line above can be rewritten as
    ##\log_3 \frac{2x + 3}{x - 2} = 2##
    So far, so good.
    In the second line it looks like you did the division this way:
    ##\frac{2x + 3}{x - 2} = \frac{2x}{x} - \frac{3}{2} = 2##
    If that's what you did, it is incorrect - that's not how you do division. For example, ##\frac{4 + 2}{2 + 1} \neq \frac 4 2 + \frac 2 1 = 2 + 2 = 4##. The correct answer is 6/3 = 2.
     
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