[awesome_dude]

The Triangle of power explanation of logarithms is what really got me across logs.

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))

[cafeinux]

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.

[awesome_dude]

That is not without humour :)

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"

[cafeinux]

I said "power" as in "exponent", so we basically have the same understanding, I just do without the triangle.