Ironically, that notation, which I just discovered, confuses me more than anything else.
Logs clicked for me when someone online said "amongst all the definitions we have for logs, the most useful and less taught is that log() is just a power". At that exact instant, it's like if years of arcane and foreign language just disappeared in front of my eyes to leave only obviousness and poetry.
I don't understand the comment about it just being a power, but, for me, knowing that it's filling in the third vertice on the triangle with exponents at the top, and n on the other is what makes it work for me - I now know in my head when I am looking for the log of n, I am looking for the exponent that would turn the log into n.
I don't go looking for the exact log, I only look for whole numbers when I am calculating the value in my mind.
But it makes sense when I am looking for the log2 of 8 to know that the answer is "what exponent will make 2 into 8"? and that's "3"
