# Homework Help: How can prove logx< x^1/2

1. Feb 9, 2010

### ha11

How can prove logx< x^1/2 for x>1

2. Feb 9, 2010

### VeeEight

What have you tried so far? Perhaps induction will work

3. Feb 9, 2010

### awkward

Here's one approach:

Define $$f(x) = \sqrt{x} - \ln(x)$$.

See if you can show that $$f(1) > 0$$ and $$f'(x) \geq 0$$ for $$x \geq 1$$.

That would do it. Do you see why?

 Oops, that won't work, because it isn't true that $$f'(x) \geq 0$$ for $$x \geq 1$$!

So try this instead-- find the minimum value of f by solving $$f'(x) = 0$$. If the minimum is positive (and it is), then you are done.

Last edited: Feb 9, 2010
4. Feb 10, 2010

thanks