Interesting problem i came acrosss

[oneomega]

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?

 

[oneomega]

a small addendum, what i actually mean by angle b/w curves is the angle b/w their tangents at that point.

 

[arildno]

a^(x)=b^(x)-->(a/b)^x=1.
What does that tell you x must be, when "a" does not equal "b"?

 

[oneomega]

you tell me, is there something wrong with this problem?

 

[oneomega]

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

 

[oneomega]

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.

 

[arildno]

That's right!

Both functions equal 1 when x=0

 

[oneomega]

i'm not this dumb usually, its just that i got stuck here. thanks a lot.