Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to calculate 167^0,2 without a calculator

  1. Jul 22, 2014 #1
    I was wondering how that could be done.


    I tried 0,2 ---> 1/5, then 167 ^(1/5) , which should lead to 5√167 (fifth root of 167) , but I can't seem to move on from there
     
  2. jcsd
  3. Jul 22, 2014 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    0,2= 1/5 so you are asking for the principal fifth root of 167. I note that [itex]2^5= 32[/itex] and [itex]3^5= 243[/itex] so I would next try 2.5. [itex]2.5^5= 97.65625[/itex] (yes, I did that "by hand"!). That's less than 167 so I would try 2.75 next and keep going until I got sufficient accuracy.
     
  4. Jul 22, 2014 #3

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I did it using the first two terms of a binomial expansion.

    $$167^\frac{1}{5} = \left( 243 - 76 \right) = 243^\frac{1}{5} \left(1 - \frac{76}{243} \right)^\frac{1}{5} \doteq 3 -\frac{1}{5} \frac{76}{81}$$
     
  5. Jul 25, 2014 #4
    Are you allowed to use log tables?
     
  6. Jul 29, 2014 #5
    I don't think so, but I'd like you to elaborate if you can solve it with log.
     
  7. Jul 30, 2014 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    If [itex]x= 167^{0,2}[/itex] the [itex]log(x)= 0,2 log(167)[/itex].

    So: look up the logarithm of 167 in your log table, multiply by 0,2 then look up the number whose logarithm is that.
     
  8. Jul 30, 2014 #7

    Borek

    User Avatar

    Staff: Mentor

    Note: you will not find logarithm of just 167. log table I have here (base 10) contains logs of numbers between 1 and 10, so you will need to express 167 as 1.67*100 and then log(167) = log(1.67)+2.

    Not that it changes the general idea, just makes it a little bit more convoluted.
     
  9. Aug 3, 2014 #8

    statdad

    User Avatar
    Homework Helper

    "log table I have here..."

    Not sure I could put a finger on a log table if pressed. It reminds me of a conversation I had many years ago (1990-ish) with a historian
    Historian: "Do you have a slide rule I can use?"
    Me: "No, I haven't had one for many years."
    Historian: "I thought every mathematician had one."
    Me: "Before you go, do you have any papyrus I could have?"
    Historian: "Why would you think we still use that?"

    He didn't get my humor.
     
  10. Aug 8, 2014 #9

    Mark44

    Staff: Mentor

    I haven't used any of mine for some time, but I still have a few slide rules around.
     
  11. Aug 8, 2014 #10

    statdad

    User Avatar
    Homework Helper

    I still have two, but they are in my house, on the same shelves as the old roll film cameras my father had 85 years ago.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to calculate 167^0,2 without a calculator
Loading...