# Thread: Use IVT to prove that arctan(x) = ln (x) has a solution for some x?

1. ## Use IVT to prove that arctan(x) = ln (x) has a solution for some x?

I understand the IVT (intermediate value theorem), and have applied it to situations involving finding the root of a solution between two x values for e.g., but I'm unsure how it applies to this situation. I tried bringing ln(x) to the other side, but unsure where to go from there. This is a question from my textbook and they give no answers so I can't check if what I've done is anywhere near correct. I considered using two nondescript values such that the solution for x lies between these, but I don't think that works entirely :S. Can anyone shed some light on this question? thanks

2. Study this function : $x\mapsto \arctan(x)-\ln(x)$.