# Finding the intersection of two graphs [duplicate]

This question already has an answer here:

I'm having difficulty with finding the intersecting point of two graphs. Here is what I have done so far:

Plot[{8*n^2, 64*n*Log2[n]}, {n, 0, 100}]


which produces the following graph: To find the intersection I tried:

FindRoot[{8*n^2, 64*n*Log2[n]}, {0, 100}, {0, 20000}]


But I got an error I think:

FindRoot::nlnum1: "The function value {{8.\ n^2,92.3325\ n\ Log[n]}[0.,0.]} is not a list of numbers with dimensions {1} when the arguments are {0.,0.}"

I am using Mathematica 10.

## marked as duplicate by Dr. belisarius, Artes, bbgodfrey, Community♦Apr 9 '15 at 14:56

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• Solve[8*n^2 - 64*n*Log2[n] == 0, n] // N – Dr. belisarius Apr 9 '15 at 14:14
• I'm sorry, have you seen FindRoot documentation page? – Kuba Apr 9 '15 at 14:15
• Possible duplicate of 74150 or 28987. – dionys Apr 9 '15 at 14:35

## 1 Answer

One approach is to set the first equation equal to the second and use Reduce to solve the system:

Block[{f1, f2, n, sol},
f1 := 8*n^2;
f2 := 64*n*Log2[n];
sol = N@Reduce[f1 == f2, n]]


(* n == 1.1 || n == 43.5593 *)

Also, you might want to check out the Mathematica tutorials on equation solving.