1. Not finding help here? Sign up for a free 30min 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!

Logarithm question, finding all possible pairs of integers

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Find all possible pairs of integers a and n such that:

    log(1/n)(√(a+√(15)) - √(a -√(15)))=-1/2

    (that's log to the base (1/n))


    3. The attempt at a solution

    (1/n)^-1/2 = (√(a+√(15)) - √(a -√(15))
    ∴ n^4 = (a+√(15) - (a -√(15) - 2√((a+√15)(a -√(15))
    ∴ n^4 = =2√(15) - 2√((a+√15)(a -√(15))
    eventually simplifying to:
    n^(16)-√(15)n^4 =4a^2

    dont know how to solve, probably made mistake

    question is from core 3 edexcel and is worth 13 marks
     
  2. jcsd
  3. Dec 3, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

  4. Dec 3, 2012 #3

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    Typing in all the steps into the Compose form would be a mess; but one of my partial results seems to give the equation,
    (n-2a)/(-2) = sqrt(a2-15)
     
  5. Dec 3, 2012 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Yeah, I get the same thing.
     
  6. Dec 3, 2012 #5

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    Further steps give me n2-4an+60=0, from which solving for a,
    a=(n/4)+(15/n).

    That could let us find possible pairs of INTEGERS for a and n.
     
  7. Dec 3, 2012 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    OK, but maybe we should let the OP solve it? :tongue:
     
  8. Dec 3, 2012 #7

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    Knowing no clever way to solve specifically for integer solutions, would a BASIC FOR loop be acceptable? I would run n from about 0.100 to 50, incrementing by 0.100 for each step. a would be calculated in each run through the loop.

    ( I know no clever, fancy way to find the integer solutions for this rational equation but I believe a BASIC program can expose some integer number pairs for n and a ).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Logarithm question, finding all possible pairs of integers
Loading...