(adsbygoogle = window.adsbygoogle || []).push({}); (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. :)

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# Intersection of two functions

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