system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 What is log and natural log??

I just don’t get it. From high school til now post college graduate, I still don’t know what logarithms are.
gpt
Suppose we have two numbers, X=2 and Y=8.

Log simply asks: how many Xs we need to multiply together to get Y?

Or in this case, how many 2s do we need to multiply together to get 8?

Since 2 x 2 x 2 = 8, the answer is 3.  We need to multiply 2 by itself 3 times to get to 8.

In math notation, we write this as logₓ(Y) or in our case: log₂(8) = 3.

Sometimes we call X (2 in our case) the "base".  It's just the number we want to multiply several times to get to Y.

Turns out, for various calculations we are interested in multiples of the *natural constant* "*e*" (2.71828...).

Rather than writing logₑ(Y) or log₂.₇₁₈₂₈(Y) every time, we just abbreviate it as *ln*(Y) where *ln* stands for "natural log".

So "natural log" is just log with base = *e*.