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Using logs in calculations

  1. Nov 9, 2006 #1
    I wish to find the value of .8^(2/5) using logs. I can find the value of .8^(-2/5) as follows: =(log(8)X1/10)X-2/5
    =(-1 + .9031)X-2/5 = (-.0969)X-2/5 = +.03876;
    antilog(.03876) = 1.093;
    Now to find .8^(2/5) my approach is the same:
    log(.8)X2/5 = (log(8)X10^-1)X2/5
    = (bar1 + .9031)X2/5 : what do I do next. (bar1 = -1)
     
  2. jcsd
  3. Nov 9, 2006 #2

    Integral

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    It is hard to understand what you have done.

    [tex]\log( .8^ \frac 2 5 )[/tex]

    [tex]= \frac 2 5 \log (.8)[/tex]
    [tex] = \frac 2 5 ( \log (8) - \log (10)) [/tex]

    Excell tells me the answer should be ~.915
     
    Last edited: Nov 9, 2006
  4. Nov 9, 2006 #3

    HallsofIvy

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    John O'Meara's work looks exactly like what I used to do in highschool. (Of course, we did all calculations on an abacus back then!). Since a table of logarithms only gave logarithms for numbers between 1 and 10, write .8 as 8 x 10-1. Then log(.8)= log(8)- 1! It's hard to imagine anyone today doing it that way- a calculator will give immediately that log(.8)= -0.096910013008056414358783315826521, far more accurate than any table would be. 2/5 times that is
    -0.038764005203222565743513326330608. (I got that, by the way, from the calculator supplied with Windows.)

    Integral, log(.8) is negative. The value you give can't possibly be right.
     
  5. Nov 10, 2006 #4

    Integral

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    Clarifcation:
    My Excell value is for [itex] .8 ^ \frac 2 5 [/itex] not the log.
     
  6. Nov 11, 2006 #5

    HallsofIvy

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    Ah! Okay.

    John O'Meara, after you have (-1+ .9031)X2/5 the obvious "next thing to do" is the multiplication: -2/5+ .36124= -.4+ .361234= -1+ .6+ .361234= -1+ .961234. Now look that up in the "body" of whatever log tables you are using: find the x that gives that logarithm. More simply you can use the calculator that comes with Windows to find the 'inverse' log of that: the inverse log of .961234 is 9.146056 so we have 9.146056x 10-1= 0.9146056. Actually, it is not at all difficult to use the Windows calculator to do .8.4 directly and see that that is, in fact, the correct answer.
     
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