# Amc 12b #20

1. Apr 6, 2006

### Jameson

Let $x$ be chosen at random from the interval $(0,1)$. What is the probability that $[\log_{10}(4x)]-[\log_{10}(x)]=0$?

Here $[x]$ denotes the greatest integer that is less than or equal to $x$.

This is multiple choice, but I don't think posting the possibilities are necessary. I would give my input to the problem of course, but I have no idea where to start.

2. Apr 6, 2006

### shmoe

First thing to do, for a given integer n work out the values of x where [log_10(x)]=n.

By the way, you want "tex" in the tags instead of "math".

3. Apr 8, 2006

### Jameson

Thanks, and I noticed by mixplaced tags as well. I copied this from my post at a site where the [math] tags are used instead of [ tex ] ones. I can't edit it now though, so if a moderator could that'd be nice.