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Formulae with logarithmic terms

  1. Jan 3, 2015 #1
    1. The problem statement, all variables and given/known data
    w = 1/h ln(l/lo-1)
    w=-2.6, lo=16 and h =1.5 Find L.
    2. Relevant equations


    3. The attempt at a solution
    Plug in the values
    2.6 = 1/1.5 ln(l/16 - 1)
    Make the log term the subject.
    ln(L/16 -1) = 1/1.5/-2.6
    ln(L/16-1) = 0.666/-0.256
    ln(L/16-1) = -0.256

    Change the log statement to an index statement

    L/16-1 = e^-0.256
    Get L on its own
    L = e^-0.256x16+1
    L = 13.386
    Am I on the right track?
     
  2. jcsd
  3. Jan 3, 2015 #2

    BvU

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    You can check by filling in the numbers, right?
    First stumble is then that L/l0-1 < 0 and you can't take the ln of a negative number.
    Conclusion: you're off the right track. Can you see where this last error popped up ?
    Correct it and try again (check by filling in the numbers)
     
  4. Jan 3, 2015 #3
    Forgot to plug in my answer! I will have another look at it. Seems like I am way off so will have to do a bit more reading into it. Thanks for the reply.
     
  5. Jan 3, 2015 #4
    Yes. Just plugged in my answer and calculator shows error. So L must be bigger than 16.
     
  6. Jan 3, 2015 #5

    BvU

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    Do this one step at a time

    Then check - and if it still doesn't fit:

    Check this step.
     
  7. Jan 3, 2015 #6
    L/16 -1 = e^-0.256

    L -1 = e^-0.256 x 16

    L = 1 e^-0.256 x 16

    L = 1 + 0.774 x 16 = 28.3284. This is also wrong when i plug it in.
     
  8. Jan 3, 2015 #7
    Is ##\frac{L}{16}-1=e^{-0.256}## EQUIVALENT TO ##L - 1=e^{-0.256} \times 16##?

    Why didn't you multiply [1] by [16] ??
     
    Last edited by a moderator: Jan 3, 2015
  9. Jan 3, 2015 #8

    SammyS

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    To make the log term the subject, why not simply multiply (both sides) by 1.5 ?
     
  10. Jan 3, 2015 #9
    I am starting to confuse myself here!

    The equation is -2.6 = 1/1.5 ln(L/Lo -1)

    multiply both sides by 1.5

    -2.6x1.5 = ln(L/16 -1)

    -3.9= ln(L/16-1)

    L/16-1 e^-39

    L/16 -1 = 0.02

    L-1 =0.02 x 16

    L = 0.02x16 +1
    L= 1.32. I know i am going wrong somewhere because my answer does not plug into the original equation?
     
  11. Jan 3, 2015 #10
    Again ,, Why don't you multiply 1 by 16 ???
    You have to multiply 16 By each term in the equation ,, RIGHT ,,!
     
  12. Jan 3, 2015 #11
    If L-1 = 0.02 x 16 Then to get L on its own does the -1 turn into 1 on the other side of the equation? I can`t see the wood for the trees on this one.
     
  13. Jan 3, 2015 #12

    -2.6x1.5 = ln(L/16 -1)

    -3.9= ln(L/16-1)

    L/16-1 = e^-3.9

    L/16 -1 = 0.02 [Multiply EACH term by 16]

    L-16 =0.02 x 16

    L = 0.02x16 +16


    To justify the answer , plug in the value of L in the original equation ,

    :)
     
    Last edited: Jan 3, 2015
  14. Jan 3, 2015 #13

    Mark44

    Staff: Mentor

    The step above is missing the =, and the step below is wrong. When you multiply both sides of the equation by 16, you need to multiply each term on the left side by 16. IOW, you have to distribute the 16 across both terms.
     
  15. Jan 3, 2015 #14
    Thanks Maged, Mark. 16.32 plugs in correctly.
     
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