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

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

This is multiple choice, but I don't think posting the possibilities are necessary.