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Log problem

  1. Jul 27, 2008 #1
    1. The problem statement, all variables and given/known data
    If logb(2)=0.4307, find logb(16)


    2. Relevant equations



    3. The attempt at a solution
    If the log has the same base can I eliminate it and solve the equation?
    If b^.04307=2 then b^?=16
    can I say 2/.04307=16/x
    16*0.4307=2x
    x=3.4456
    Am I close or have I missed something obvious?
     
  2. jcsd
  3. Jul 27, 2008 #2

    tiny-tim

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    NO!

    Hint: 16 = 2 x 2 x 2 x 2. :smile:
     
  4. Jul 27, 2008 #3
    Okay, 2^4=16
    If I have b^.4307=2 By trial and error, I came up with 5 for b. 5^.4307=2 or log5(.4307)=2
    Specifically, what steps do I follow to discover what the base is without resorting to a trial and error method.
    Thanks
     
  5. Jul 27, 2008 #4

    Avodyne

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    Start with b^.4307=2, and raise both sides to a certain power, such that you will get 16 on the right.
     
  6. Jul 28, 2008 #5

    tiny-tim

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    Hi yoleven! :smile:

    You don't need to find b … the question doesn't ask you for b.

    Hint: 16 = 2 x 2 x 2 x 2.

    logb(pq) = logb(p) + logb(q) :smile:
     
  7. Jul 28, 2008 #6

    HallsofIvy

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    Or, more simply for this problem log(ab)= b log(a).
     
  8. Jul 28, 2008 #7

    tiny-tim

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    oooh … that's far too advanced! :wink:
     
  9. Jul 28, 2008 #8
    If logb(2)=.4307
    logb(16)=1.7228
    because if b^.4307=2, (b^.4307)^4=(2)^4
    b^1.7228=16
    Okay? Thanks again.
     
  10. Jul 28, 2008 #9
    1.7228 is correct.
     
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