## owlet one year ago Find the intersection of $$x^3$$ and $$3^x$$ How to do it?

1. zzr0ck3r

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

2. owlet

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

3. zzr0ck3r

Are you asking me if 3^3 = 27?

4. owlet

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

5. owlet

6. zzr0ck3r

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

7. zzr0ck3r

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

8. zzr0ck3r

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

9. owlet

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

10. zzr0ck3r

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