Decay rates in exponential decay

Hi there, I'm actually trying to write a little computer program which will invlove me using a half-life type of decay, and I'm not really sure how to go about various calculations.

What I want to calculate is a particular value, x, to repeatedly multiply my decaying variable Alpha by (Alpha is given and can be between 0.01 and 1), so that over 1000 steps Alpha becomes 0.01.

Now, I did this by hand for an initial alpha of 1 and got a value 0.995405418.

I'm thinking that could possibly boil down to

0.01 = Alpha ( x ^ 1000)

But I don't have the math skills to rearrange for x, and I'm not sure that's the right answer anyway.

Any pointers?