- #1
jjou
- 64
- 0
(Problem from practice math subject GRE exam:) At how many points in the xy-plane do the graphs of [tex]y=x^{12}[/tex] and [tex]y=2^x[/tex] intersect?
The answer I got was 2, but the answer key says 3.
Intuitively, by the shape of their graphs, I would say two. I tried to calculate actual values for x:
[tex]2^x=x^{12}[/tex]
[tex]x\ln2=12\ln x[/tex]
[tex]\frac{\ln2}{12}=\frac{\ln x}{x}[/tex]
[tex]\sqrt[12]{2}=\sqrt[x]{x}[/tex]
I don't know what to do with that last equation.
I'm really confused though, because I can't even imagine how they would get a third intersection. Any help would be appreciated. :)
The answer I got was 2, but the answer key says 3.
Intuitively, by the shape of their graphs, I would say two. I tried to calculate actual values for x:
[tex]2^x=x^{12}[/tex]
[tex]x\ln2=12\ln x[/tex]
[tex]\frac{\ln2}{12}=\frac{\ln x}{x}[/tex]
[tex]\sqrt[12]{2}=\sqrt[x]{x}[/tex]
I don't know what to do with that last equation.
I'm really confused though, because I can't even imagine how they would get a third intersection. Any help would be appreciated. :)