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Estimate the values of log(4)

  1. Dec 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Given that log(2) is roughly 0.30 and log(∏) is roughly 0.5, estimate the values of log(4), log(5), log(6) and log(8).


    2. Relevant equations
    log(ab)=log(a)+log(b)
    log(a/b)=log(a)-log(b)
    log(a^n)=nlog(a)


    3. The attempt at a solution
    I found log(4) and log(8) using log(2)+log(2) [+log(2)], and i estimated log(6) using log(2)+log(∏), but i don't know how to get to log(5).
     
  2. jcsd
  3. Dec 5, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi k3r0! :smile:

    hint: log(125) ? :wink:
     
  4. Dec 5, 2013 #3

    Mark44

    Staff: Mentor

    My guess, assuming there isn't a mistake in the problem statement, is that they want you to use linear interpolation. log(5) ≈ (1/2)(log(4) + log(6)). This would be the average (or mean) of the two log values.
     
  5. Dec 5, 2013 #4
    Thanks a lot, that method never crossed my mind. I spent about half an hour being irritated at that question, haha.

    Thanks!
     
  6. Dec 6, 2013 #5
    another hint: what is [itex]\pi^2[/itex] equal to?
     
  7. Dec 7, 2013 #6
    log(5)=log(10)-log(2) = 1 - log(2) = 0.7
     
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