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!

Logarithms and triangles help

  1. Nov 28, 2006 #1
    1. The problem statement, all variables and given/known data

    Define a, b, and c as the sides of a right triangle where c is the hypotenuse, and a > 1 and c > b+1

    show that
    [tex]log_{c+b} a + log_{c-b} a = 2(log_{c+b} a)(log_{c-b} a)[/tex]

    2. Governing equations

    3. The attempt at a solution
    Should I assume that a=2 and c=b+2?!
    Last edited: Nov 28, 2006
  2. jcsd
  3. Nov 28, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    What did Mr. Pythagoras say about "the sqaw on the hippopotamus"?
  4. Nov 28, 2006 #3
    c²=a²+b²....but then how do I apply that to the given statement. Perhaps if you give me a hint, I will manage to finish off the question.
  5. Nov 28, 2006 #4
  6. Nov 29, 2006 #5


    User Avatar
    Homework Helper

    I haven't got time to look at it now, but maybe it would be useful, as mentioned above, to use a^2 = c^2 - b^2 = (c - b) (c + b), and the fact that [tex]\log_{a}x^n = n\log_{a}x[/tex] somehow.
  7. Nov 29, 2006 #6


    User Avatar
    Science Advisor
    Homework Helper

    OK, here's the strategy I used to get a handle on this.

    First off, it's a totaly weird looking equation. I cant think what practical use it would be. The things in there are "a", "c+b" and "c-b" It's also got logs to two different bases in the same equation.

    I tried putting in the numbers for some rightangled triangles like 3,4,5 and 5,12,13. That didn't help much.

    What else are you given? some weird stuff, a > 1 and c > b+1 or c-b > 1. Hm... maybe that's just saying all the "interesting" things are positive numbers so the logs are well defined. I dunno what else to do with it yet, so forget about it till later...

    What else do we know? Well, a^2 + b^2 = c^2 is the only equation you have. So try and work forwards from a^2 + b^2 = c^2, and backwards from what you are trying to prove, and see if you can meet up in the middle.

    From a^2 + b^2 = c^2 we want some stuff with c+b, c-b, and some logs in it. OK...
    a^2 = c^2 - b^2 = (c+b)(c-b)
    2 ln a = ln (c+b) + ln(c-b)

    ... that looks promising but all the logs are to the same base (e). So what happens if you work backwards from the answer and transform all the logs into natural logs? The standard formula is log(base p)q = ln(q)/ln(p).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Logarithms and triangles help
  1. Help with logarithms (Replies: 4)

  2. Logarithm [Help] (Replies: 1)

  3. Logarithm Help (Replies: 5)

  4. Logarithms help (Replies: 3)

  5. Help With Logarithms (Replies: 5)