9768 #63

[YKM]

Dear all,

At how many points in the xy-plane do the graphs of y = x^12 and y = 2^x intersect?

The answer is 3.

Can anyone tell me why?

Thanks
YKM

[hadimotamedi]

It reduces to :
ln(x) = ln2/12 x
So must find the intersect between the ln(x) curve and the x curve .

[YKM]

Thanks, I am aware that ln(x) = x{ln(2)/12}, the left hand side is the curve represented by y = ln(x), we all know how it looks like, and the right hand side is a straight line. To me, at most they can only intersect each other two times, how can it intersect threes times?....this is not possible.......

[hadimotamedi]

If you sketch the plots on MATLAB, you will see two intersection points (the one you have concluded to).

[blitzer6266]

There is a definite problem with this approach. There is an intersection when x is negative which you lose when you mess with logs. I think you just have to keep it simple and look at the behavior of the graphs as given. There will clearly be two intersections when x is relatively small. Then 2^x grows more quickly than a polynomial, so you know there has to be another intersection when x is larger. This gives 3 total intersections.

[DDswife]

It reduces to :
ln(x) = ln2/12 x
So must find the intersect between the ln(x) curve and the x curve .

I think that you need an absolute value for the log