Find the intersection of $x^3$ and $3^x$
How to do it?

Question

Find the intersection of $x^3$ and $3^x$
How to do it?

zzr0ck3r · Answer

Hint for one solution:

$a^a=a^a$.

The other solution gets a little tricky. Google "analytic continuation of the product log function"

owlet · Answer

so x=3? one point of intersection would be (3, 27) ?

zzr0ck3r · Answer

Are you asking me if 3^3 = 27?

owlet · Answer

no, if one of the intersection points of these two function would be (3, 27)

owlet · Answer

how about the other point?

zzr0ck3r · Answer

put in $x=3$ on both functions, and then see what you get out...

zzr0ck3r · Answer

As far as the other point, I refer you to my first comment.

zzr0ck3r · Answer

The solution is transcendental, so like $\pi$ there is no good way to explain it with numbers :)

owlet · Answer

oh got it. thanks.. no point of solving this thing because its too complicatedlol
 but I understand the first solution though :) tysm

zzr0ck3r · Answer

yeah, it is crazy. There actually might be infinite solutions, but only one is algebraic, meaning we can express it with numbers and symbols...