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9768 #63

Posted: Mon Aug 08, 2011 10:39 am
by 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

Re: 9768 #63

Posted: Tue Aug 09, 2011 12:30 am
by hadimotamedi
It reduces to :
ln(x) = ln2/12 x
So must find the intersect between the ln(x) curve and the x curve .

Re: 9768 #63

Posted: Tue Aug 09, 2011 10:27 am
by 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.......

Re: 9768 #63

Posted: Wed Aug 10, 2011 4:41 am
by hadimotamedi
If you sketch the plots on MATLAB, you will see two intersection points (the one you have concluded to).

Re: 9768 #63

Posted: Thu Aug 11, 2011 2:48 am
by 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.

Re: 9768 #63

Posted: Sat Aug 23, 2014 7:38 pm
by DDswife
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