Not quite. Ages are usually counted from 0. ln(0) is undefined, but after that from the first moment after birth until some time in its 52nd day, a dog's age is negative in dog-time (that's probably why it's considered important for the puppy to remain with its parents during this period; a negative-aged dog on its own is like a naked singularity). Then from day 52 to the end of its first year, the dog will age from 0 to 31.

The other end of the scale is surprising too: 200 human years is less than 116 dog years.