1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Base 10 log question

  1. Sep 29, 2008 #1
    Is there a way to calculate multi digit base 10 logs without a calc or tables?

    eg.. what is ? log (base 10) of 1381.42?? (without a calulator)??
  2. jcsd
  3. Sep 29, 2008 #2
    (with caveat that i memorized log 1 - 9)
  4. Sep 30, 2008 #3


    User Avatar
    Homework Helper

    Of coursethat is possible, the first people who made tables did not have calculators.
    numbers should be decomposed multiplicatively.
    One method is to factor into primes
    This shows a problem logs of many primes will be needed
    another method would involve writing the number as a product of factors with known logs and factors near 1 since when x is small
    say one knew log(138176)
  5. Sep 30, 2008 #4


    User Avatar
    Science Advisor

    What I would do is this:
    First, log(1381.42)= log(0.138142 x104)= 4+ log(0.138142).

    Now, use the 'Taylor's Polynomial' expansion:
    for 0< x< 1, log(x)= x+ (1/2)x2+ (1/3)x^3+ ...+ (1/n)x^n.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook