You may have never seen fractional powers. Let's continue to do that. All of the numbers between 1 and 10 are fractional powers of 10. 2 has a log of .30103. That's all there is to it.
Logs are powers.
I also got 5.52525 as a log. I looked up .52525 in my log tables, and I got 3.35100. Your scientific calculator can show more accuracy than that. But that is pretty good anyway. There are other bases, besides 10, for logs.