Logarithmic question

I've got a random number between 0 and 1 (simple Rnd() function). If the number is less than 0.1, I need to know how many times you'd need to multiply 0.1 by 0.9 to get under the value I have. I also need to know the reverse. That is, the same number of multiples of some number (which I can't even guess at) will get you closer to 1 without going over.

I'm sure it's going to be based on math.log10 function, but I don't know how...