I do not know if you have noticed that it is increasingly difficult to level up or reputation in Steemit. Investigating in the network I found out what Steemit does to give you the reputation within the platform and as you suspect, it is logarithmic, meaning that as you go up the level it costs much more to reach the next one.
Steemit reputation points are calculated using the base 10 log functions. It is easy to increase your reputation score at the beginning, but the higher your reputation, the harder it will be to increase it. It is approximately 10 times more difficult from 1 point to another. A level 50 reputation is 10 times stronger than a reputation of 49.
There are 2 types of points: simplified and complete. The one in your Steemit profile that has 25 when it starts is not the actual value stored in the Steem blockchain. It's just a simplified reputation score. Your reputation score is real values in large numbers instead of a simple double-digit reputation score. Your scores can be found at https://steemd.com/@username.
The calculation of the simplified score is as follows:
Take out the Log10 from the reputation that appears in https://steemd.com/@username. Subtract 9, Multiply by 9, Add 25 and round to the nearest integer.
Here is a scoreboard to check how many points are needed for the next level.