Dear all,
At how many points in the xyplane do the graphs of y = x^12 and y = 2^x intersect?
The answer is 3.
Can anyone tell me why?
Thanks
YKM
9768 #63

 Posts: 34
 Joined: Thu Dec 30, 2010 4:36 am
Re: 9768 #63
It reduces to :
ln(x) = ln2/12 x
So must find the intersect between the ln(x) curve and the x curve .
ln(x) = ln2/12 x
So must find the intersect between the ln(x) curve and the x curve .
Re: 9768 #63
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.......

 Posts: 34
 Joined: Thu Dec 30, 2010 4:36 am
Re: 9768 #63
If you sketch the plots on MATLAB, you will see two intersection points (the one you have concluded to).

 Posts: 61
 Joined: Sun Apr 04, 2010 1:08 pm
Re: 9768 #63
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.
Re: 9768 #63
hadimotamedi wrote: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