Interesting problem i came acrosss

  1. okay,
    there are two curves: curve1: y=a^x and curve2: b^x. what is the angle between them at their point of intersection. given that (a≠b).
    My general method:
    if i wanted angle b/w the curves y=x^2 and y=(x-2)^2, i would easily do it.
    let A be angle b/w them,
    then, tanA= [tan(m1)-tan(m2)]/1-tanm1.tanm2
    can be used at their point of intersection.this is what my textbook says. but the problem with a^x and b^x is that I CANNOT FIND THE POINT OF INTERSECTION. which brings me to the very basic question, how can we find pt of intersection of curves like this?
     
  2. jcsd
  3. a small addendum, what i actually mean by angle b/w curves is the angle b/w their tangents at that point.
     
  4. arildno

    arildno 12,015
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    a^(x)=b^(x)-->(a/b)^x=1.
    What does that tell you x must be, when "a" does not equal "b"?
     
  5. you tell me, is there something wrong with this problem?
     
  6. beacuse, at the same x point, a and b has to be equal to get you to the same y value as the equation suggests
     
  7. oh wait, i got it, x mustt be zero, so that for diff values of a and b, they get you the same y value.
    i got it now.
     
  8. arildno

    arildno 12,015
    Science Advisor
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    That's right!
    :smile:
    Both functions equal 1 when x=0
     
    1 person likes this.
  9. i'm not this dumb usually, its just that i got stuck here. thanks a lot.
     
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