what does log mean and what is it?

File: image.jpg (262KB, 1200x1200px) Image search: [Google]

262KB, 1200x1200px

log

>>8747282
log is the inverse of the exponential function.
For instance 2^3 = 2*2*2 = 8
Lets say you had the base (2) and the result, (8) and you wanted to find out what power 2 was set to to equal 8, you would take a log.

log2(8) = 3

>>8747294
Honestly a better explanation for log than most high school teachers

>>8747282
BAD DOG
NO LOG FOR YOU.

>>8747282
If I recall correctly, it rolls down stairs, alone or in pairs. It has even been known to roll over your neighbors dog.

[math] \log(x) := \int_1^x \frac{1}{t} \, {\mathrm d} t [/math]

The function fulfills

[math] \log(x)' = \frac{1}{x} [/math]

[math] \log(1) = \int_1^1 \frac{1}{t} \, {\mathrm d} t = 0 [/math]

[math] \log(e^x) = \int_1^{e^x} \frac{1}{t} \, {\mathrm d} t = \int_1^{x} e^{-x} \, e^{x} {\mathrm d} x = x [/math]

etc.

>>8747294
someone not being a cunt on (((ANY BOARD))) when someone asks for help, esp. regarding a trivial matter

ure a bro, man

>>8747282
It's a homomorphism between the multiplicative group of positive real numbers and the additive group of real numbers.

>>8747323
You make out /sci/ worse than it is

>>8747327
I imagine it's the only nontrival one?

>>8747323
To be fair, /sci/ is one of the friendliest boards when it comes to actual help in my experience.

Consider a Lie group [math]G[/math] with Lie algebra [math]g[/math]. Each [math]X\in g[/math] determines a unique left-invariant vector field, which we will also denote by [math]X[/math]. The flow [math]\gamma_X[/math]of this vector field gives rise to the definition of the exponential map [math]\exp \colon g \to G[/math] via [math]\exp (X) = \gamma_X (1)[/math]. There are neighborhoods [math]0 \in U \subset g[/math] and [math]e \in V \subset G[/math] such that [math]\exp[/math] is a diffeomorphism between these sets. Its inverse [math]\log \colon V \to U[/math] is called the logarithm.

>>8747327
Wait really? Neat

>>8747282
Stop posting anime.

>>8747362
[math] h(b_1(x,y)) = b_2(h(x),h(y)) [/math]

[math] \log(x\cdot y) = \log(x) + \log(y) [/math]

[math] h=\log [/math]
[math] b_1 = \cdot [/math]
[math] b_2 = + [/math]

[math] \log(x) = -{\mathrm {Li}}_{1}( 1-x ) [/math]

where [math] {\mathrm {Li}} [/math] is the polylogarithm.

>>8747335
>I imagine it's the only nontrival one?
It would have to be wouldn't it? (up to scaling/change of base)