Thread: How to solve this IVT problem??

How do I solve this problem?

Use IVT (Intermediate Value Theorem) to prove the following statement:

2^x = bx has a solution if b>2

Please help me solve this problem.

Attempt: I know that IVT says that a continuous function has values in every single points, but if I don't the value in front of x how am I supposed to solve that?

Originally Posted by skboss

How do I solve this problem?

Use IVT (Intermediate Value Theorem) to prove the following statement:

2^x = bx has a solution if b>2

Please help me solve this problem.

Attempt: I know that IVT says that a continuous function has values in every single points, but if I don't the value in front of x how am I supposed to solve that?

Let f(x)= . Then f(1)= 2- b< 0. Whatever b is, there exist n such that . For that n, .

Now use the IVT

Originally Posted by HallsofIvy

Let f(x)= . Then f(1)= 2- b< 0. Whatever b is, there exist n such that . For that n, .

Now use the IVT

Thank you very much, but I got lost after the 2nd step when u introduce n. If you can explain that, that would be great. Thanks again.

Why part do you need explained?

Do you understand why I wanted to be able to say that f(1)< 0 and that f(some number) > 0?

Do you understand why ?