>>12536909>Logarithms are a bitch though, they make zero sense>>12536968logarithms make a lot of sense if you look at them the right way. They are a way of changing the "scale" of numbers from additive (1,2,3,4,5....) to multiplicative.
What does that mean?
On a normal scale (1,2,3,4....), addition and subtraction of the same number is the same "distance" on the scale. You have the number 20, and subtract 10, you get 10; you add 10 instead, you get 30. In both direction, you move a "distance" of 10 (either up or down, subtraction or addition).
Now, what happens if you divide or multiply vy the same number? take 20 divided by 5, and compare to multiplying 20 by 5.
You go from 20 to 4, so -16 "distance" on the scale when you divide; but when you multiply, you go from 20 to , 100 so +80. -16 and +80 are not the same "distance" on the scale, even though you multiplied/divided by the same number (2).
Log scale converts everything to a scale where multiplication/division by is the same "distance" on the scale.
So, if you take the natural log (ln) of 20, you get ~2.99. The ln of 4, which is 20/5, is ~1.38. The ln of 100, which is 20*5, is ~4.6.
The distance from 100 to 20 is ~1.61, and the distance from 20 to 4 is ~1.61, the exact same distance. So on this scale, any number X multiplied by another number Y is the same distance as X divided by Y.
The base "doesn't matter" in a sense; the difference is the same, just the absolute number changes (obviously the base can be important in some problems when you care what the actual numbers are; base2 is used in information theory for information in "bits", natural log for other purposes, etc).
