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Predicting number of digits with logarithms

  1. Jul 3, 2012 #1
    If log103 =0.477 then the number of digits in 340 will be?

    100.477 = 3
    10(0.47740)=340
    hm...?
     
  2. jcsd
  3. Jul 3, 2012 #2

    haruspex

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    340 = (100.477)40 = 100.477*40
     
  4. Jul 3, 2012 #3

    chiro

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    Hey Kartik and welcome to the forums.

    Using log laws, we know that we wish to find log_10(3^40) which gives us the number of decimal digits required to represent 3^40.

    Using log laws we first apply log_10(3^40) = 40log_10(3). Now you are given log_10(3), but in future if you wish to find log_b(x) where b is not the natural base e you use the relatioship log_b(x) = ln(x)/ln(b) where ln(x) is the natural logarithm of x and ln(b) must be non-zero (i.e. b can't be 1 or close enough to it for practical purposes).
     
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