## 9768 #63

Forum for the GRE subject test in mathematics.
YKM
Posts: 45
Joined: Mon Aug 08, 2011 10:25 am

### 9768 #63

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

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 .

YKM
Posts: 45
Joined: Mon Aug 08, 2011 10:25 am

### 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).

blitzer6266
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.

DDswife
Posts: 161
Joined: Thu Aug 14, 2014 5:29 pm

### 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