AMC 12B 2006 Problem 20

Let x be chosen at random from the interval (0,1). What is the probability that

\left\lfloor\log _{10} 4 x\right\rfloor-\left\lfloor\log _{10} x\right\rfloor=0 ?

Here \lfloor x\rfloor denotes the greatest integer that is less than or equal to x.

Answer Choices
A. \dfrac{1}{8}
B. \dfrac{3}{20}
C. \dfrac{1}{6}
D. \dfrac{1}{5}
E. \dfrac{1}{4}