Find all points of intersection between two functions

syms x 
ezplot(@(x)x^6 ,[-10,10,-10,10])
hold on
ezplot(@(x)3^x ,[-10,10,-10,10])
hold off

I have functions f(x) = x^6 and g(x) = 3^x. I made the graph of two functions, but is there any ways that I can find all points of intersection between two functions?

Answer 1

[Star Strider]

There are only 2 real intersection points. To find them, you simply need to find out the x-values where the functions equal each other, or equivalently where the difference between them is 0:

intsx = solve(x^6 == 3^x , x)

or:

intsx = solve(x^6 - 3^x == 0 , x)

then:

intsxn = vpa(intsx)

giving the 2 real roots:

intsxn =
                                          1.2593399329995780507387959662256
                                         -0.8550750819209264565809050645918

and 4 complex roots.