Any mathfags want to tell me what the fuck a logarithm is

Any mathfags want to tell me what the fuck a logarithm is
>be in calc I
>still don't know what the fuck these faggots do
>they're like powers but not
>why not just use powers
>what the fuck is e and why is it related to logs
>excuse my autism

Logs are used when you have the base and the end result but want to find the power

Like how a tuning fork has a frequency, logs have a rhythm that trancends time.

okay fucker lets say you want log(basea) b
at what power you rise a to make b

4 ^ 2 = 16
sqrt(16) = 4

Now I have the number 2 and 16. How do I get 4?

a^b=c log_a(c)=b

literally exactly what I needed to hear thank you user now can you tell me what the fuck the difference between ln and log is and wtf e is used for? here's some oc for your time

subtraction is the reverse of addition.
division of the reverse of multiplication.
logarithms are the reverse of exponents.

using log(4)16

not sure if bait or really shit at math

I'm gonna try to explain it
Basically the idea is that every positive number x can be written as x = e^y
e is a universal constant (like pi) and e = 2.718 approx.
y is called the log of x, it's the power you need to raise e to to get x.
These fuckers are useful for studying problems like population growth and also the exp function has some nice properties that make it useful for calculus in general.
Hope i helped user

Wait I'm retarded with log(2)16

e is the natural number

literally wikipedia this shit bro

not bad at math just a lil retarded and never quite grasped logarithms ask me to find derivatives or integrals and I'm good

Think of e like PI, just some special magic number. Then lookup ln(e) and that magic number

doesn't matter it was a thinking excercise for OP

whats the derivative of ln

for example
10^2=100
logbase 2 of100=10
logbase 2 of (10^2)=10
so in english, log base 2 of 100 is asking: what number do i need to exponent to the power of 2 to get 100. eg. x^2=100? x=10

nope, radicals

1/x

thank you based user more oc for being helpful

That user again, I think ln is log base e,
Not sure what it's used for though

ln means log base e, so
log(e) X = ln X

log by itself implies base 10
log(10) X = log X

Otherwise, in log base (specified number), the number you specify will be your base

log(b) X

Ok so you have powers where like a^x=b, right?
Now what if we want to find out, WHAT x do we need so that when a^x=b?
Well, we use log for that, for example in the equation above (a^x=b) we can use log as follows: log(b) in base a = x
And this is how we find x pretty much.
Lets say you're a programmer and you want to find out at which power you need to raise 2 in order to get 1028. Well, you do log(1028) base 2 and you get 10, so now you know 2^10=1028.

ln (natural logarithm) is pretty much like log, but the base every time is e, which is a constant (it stands for the sum of (1/n!) where n is all the natural numbers). So whenever we use ln we ask ourselves: At WHICH power we need to raise e IN ORDER to get some already known number?
Dunno if it explains it, it's a pretty short explanation. As to why we need it? Well, some formulas in comp-sci and engineering require logs and lns (in comp-sci lots of lgs).

forgot to mention that ln, or log(e), is commonly known as the "natural log", because e is its base.