1. The problem statement, all variables and given/known data Use the Intermediate Value Theorem to show that the equation 2^x=3x has a solution c element of (0,1) 2. Relevant equations 3. The attempt at a solution Ok I know this theorem is usually very easy, but I've never done one where I couldn't easily solve for x and plug in the end points to look for a sign change. I already graphed 2^x and 3x on my calculator and found that there is a solution in (0,1) now I just need to prove it. My only thoughts were this let f(x)= 2^x Let g(x) = 3x f(0)=2^0=1 and f(1)=2^1=2 g(0)=3x0=0 and G(1)= 3x1=3 f(0)>g(0) and f(1)<g(1) so this means at some point they must cross each other and there must exist c element of (0,1) such that 2^x=3x. Is this even right at all or anyone have a better idea?