Is This a Valid Probability Mass Function?

The first-digit law, or Benford's Law, states, according to Wikipedia, that in "many naturally occurring collections of numbers the leading significant digit is likely to be small. For example, in sets that obey the law, the number 1 appears as the most significant digit about 30% of the time, while 9 appears as the most significant digit about 5% of the time."

$P(D=j)= log_{10}\left ( \frac{j+1}{j} \right ), for j\in \left \{ 1,2,3,...,9 \right \}$

with D being the first digit. Is this a valid PMF?

$ \sum_{j=1}^{9}log_{10}\left ( \frac{j+1}{j} \right )=  \sum_{j=1}^{9}log_{10}\left ( j+1 \right )-log_{10}\left ( j \right )$

= 1.

Also, the sum is non-negative, so yes, it is a valid PMF.