https://mathcenter.oxford.emory.edu/site/math108/logs/
Some people have suggested the "triangle of power".
Some people have suggested the "triangle of power".
The notation conveys no information at all, and provides no means of proving anything, and even the notation for function composition is worse.
Given the operator pow : R^2->R there are 2 possible inverses. root and log
root isn't even interesting. its just pow with the 2nd argument precomposed with reciprocal. root x b = pow x 1/b
It wasn't until seeing the triangle and having the relationships explained that I had any clue about logarithms, up until then logs had been some archaic number that meant nothing to me.
Because of the triangle of power, I now rock up to B and B+ Trees and calculate the number of disc accesses each will require in the worst case, depending on the number of values in each block (eg, log2(n), log50(n) and log100(n))
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"