The basic formula of logarithm is already available, and yours should be derived from this basic formula.
More complex formulas will appear in the form of theorems if they appear many times in mathematical research. If it is not a necessary formula, at most, there will be a big problem.
Therefore, in the process of mathematics learning, I often find that the book Theorem is helpful for learning, but if I am complacent and even fantasize that it will become famous all over the world as soon as it is published, it is harmful to send it directly (I was so stupid for a while, which is understandable).
So show the formula you found and let's see if it already exists (I can guess which formula you found), but you just don't know it. Secondly, we can evaluate whether this formula has broad significance.
what do you think?