how to show that if the leading number of a random variable follows a uniform distribution then it's scale variant

Question

I'm now dealing with Benford's distribution. My task is to show that if the leading number of a random variable follows a uniform distribution, then it's scale variant(if we change the units of the measurement, the distribution changed). My first approach to this problem is that I think I need a way to represent the first digit of a random variable, however, I'm stuck now. Do I need to deal with some sort of floor functions? Any help? Thanks