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Rearranging logs

  1. Feb 8, 2017 #1

    Physics Dad

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    Please excuse my ignorance for posting this question, but I am confusing myself here. All I want to know is if I am rearranging this equation properly to find the value required...

    Question

    I want to rearrange the following equation to make F1 the subject.

    Equations
    m1-m2=-2.5log10(F1/F2)

    My Thinking

    So rearranging the above formula for F1 it becomes:

    F1=10-(m1-m2)/2.5 x F2

    When it comes to rearranging logs (one of the most straight forward and simple things, I know) I find myself easily confused.

    Please don't tell me the correct arrangement if I am wrong, just a little guidance please.

    Thank you in advance!
     
  2. jcsd
  3. Feb 8, 2017 #2

    berkeman

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    That doesn't look right to me.

    Start by moving the -2.5 to the LHS. Then you have log_10() on the RHS, so raise both sides to 10^() to get rid of the log term...
     
  4. Feb 8, 2017 #3

    Physics Dad

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    Thanks,

    So basically raise everything to 10, get rid of the logs, rearrange, take everything to the 10√ ?

    F1=-F2(m1-m2/2.5)

    Or is that silly?
     
  5. Feb 8, 2017 #4

    berkeman

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    No, not close. Try showing each step that I mention in my first reply, and then continue with the algebra after that. Please show each step separately so we can check it.
     
  6. Feb 8, 2017 #5

    Physics Dad

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    OK, thanks....

    So here goes:

    m1-m2=-2.5log10(F1/F2)

    -(m1-m2)/2.5=log10(F1/F2)

    F1/F2=10-(m1-m2)/2.5

    Is this right so far?
     
  7. Feb 8, 2017 #6

    berkeman

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    Yes!
     
  8. Feb 8, 2017 #7

    Physics Dad

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    so to finish it off it would be:

    F1=(F2)(10-(m1-m2)/2.5)

    ?
     
  9. Feb 8, 2017 #8

    haruspex

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    Yes.
     
  10. Feb 8, 2017 #9

    Physics Dad

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    That's great, thank you so much for your help here.

    I am sure it was frustrating for you, but it really helped me!
     
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