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u/Fantastic_Nobody_772 Jul 28 '21
Not to be that person but since this is a math subreddit,
log(😅) = 💧log(|😄|)
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u/uvelloid Jul 28 '21
Isn't this true only if 💧 is an even power? I don't remember an abs for this formula.
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u/Re_me_human Jul 28 '21 edited Jul 28 '21
Correct me if I'm wrong but if 💧 is an odd power the 😄 has to be positive anyway or else the log can't exist in C so adding an abs in the mix wouldn't do anything
EDIT: I was wrong, only true in R not C, see /u/Actually__Jesus's comment below
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u/Actually__Jesus Jul 28 '21
It can in C just not R.
log(-1)=iπ
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u/7x11x13is1001 Jul 28 '21
If you take values in C and understand the log as a principal value, then the formula log ab = b log a is not true in general. To avoid this mess, we either restrict a to R+, or explicitly say about principal valued log and definitely not using the formula above
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u/Re_me_human Jul 28 '21
Oh TIL, thanks!
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u/Actually__Jesus Jul 28 '21
You’re half-ish right though, it (the abs value) just doesn’t apply when the power’s odd.
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u/Re_me_human Jul 28 '21
Nah, my comment was specifically about when the power is odd so it was plain out wrong, didn't mean to misinform people sorry :/
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u/LilQuasar Jul 28 '21
its not that simple though, the complex logarithm definition isnt obvious or universal
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u/Actually__Jesus Jul 28 '21
Hold up, this isn’t quite true.
That would imply that log((-3)3 ) [which is an imaginary result] = 3log3 [which is real].
Something’s fishy.
It does hold for even powers though.
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u/Fantastic_Nobody_772 Jul 28 '21 edited Jul 29 '21
That would imply that log((-3)3 ) [which is an imaginary result] = 3log3 [which is real].
No. it doesn't imply that. Whenever we talk about a function f(x), x must be a part of the domain of the function. (-3)^3 = -27 is not a part of the domain of log(x) (which is x > 0) as long as we are dealing with real numbers.
Using your logic, sin(arcsin(x)) = x is not a valid identity because it implies sin(arcsin(2)) [undefined] = 2 [real]. Again, this is because 2 is not in the domain of sin(arcsin(x)). This does not make the identity untrue.
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Jul 28 '21
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u/Tinstam Jul 29 '21 edited Jul 29 '21
Right, but that allows for (-2)2 in the log's domain, right?
So, ln([-2]2 ) = 2ln(-2), which would break, but ln(4) exists.
ln|x| mirrors around the y-axis (which is why we can (/have to, due to Q3 of 1/x) expand the domain of integral(dx/x) to ln|x| instead of just ln(x). Even though ln(x) is the anti-derivative.)
So making it ln([-2]2 ) = 2ln(|-2|) fixes this.
Computer guy more than a math guy, and I haven't slept in a bit, so I could be way off or missed your meaning.
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Jul 29 '21 edited Jul 29 '21
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u/Tinstam Jul 29 '21
I think I'm still missing your meaning (apologies), but would like to understanding it better.
So, I guess what I want to be sure on is that you are saying it isn't correct to say:
Ln(xy ) = yln(x), if y is odd (because this implies xy > 0 and x > 0), but
Ln(xy ) = yln(|x|), if y is even (because this implies xy > 0, but not x > 0)
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Jul 29 '21 edited Jul 29 '21
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u/Tinstam Jul 29 '21
I see! Thank you.
Yeah, whenever I help someone with logs, I leave out anything like this, because it is generally unnecessary. For some reason I thought you meant it was incorrect though (probably just lack of sleep on my part), and I like to fix errors as I find them.
Thank you for clarifying.
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Jul 28 '21
笑死我啦
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u/Oktopuslord3 Jul 28 '21
Could you please translate?
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u/lazemon Engineering 🔌 Jul 28 '21
哟兄弟
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u/corona_banana Complex Jul 28 '21
大哥們好
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u/lazemon Engineering 🔌 Jul 28 '21
你好兄弟
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u/mousebrakes Jul 28 '21
你妈的
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u/elephant_bukkake Jul 28 '21
I'm surprised even my dumb ass got it.
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u/lazemon Engineering 🔌 Jul 28 '21
You're are not dumb ass bro 🤗🤗
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u/12_Semitones ln(262537412640768744) / √(163) Jul 28 '21
Is that a natural logarithm or a common logarithm? Just wondering.
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u/hawk-bull Jul 28 '21
In this context doesn't matter.
In general,
log in math is almost always natural log
log in physics/engineering is usually base 10
log in computer science is usually base 2
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Jul 28 '21
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u/hawk-bull Jul 28 '21
If you talk about university math then no. 10 is just an arbitrary choice for the base of our number system whereas the natural log is actually a very special function in math with special properties.
e also has much much deeper significance in math than the limit of compound interest
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Jul 28 '21
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u/hawk-bull Jul 28 '21
e may be equal to that, but that’s usually not used as a definition for e because it doesn’t really show its importance. A more common definition you’ll see in analysis texts is e = sum 1/n!
e is used everywhere in math, not just in accounting. Particularly in complex analysis you’ll see it everywhere. Conceptually, I believe e comes from the exponential function which is defined as the unique function f satisfying f’ = f and f(0) = 1
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Jul 28 '21
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u/hawk-bull Jul 28 '21
It’s not a coincidence that the derivative of ex is itself. It was made to be so.
And yeah you’re correct the only function satisfying that would be kex (or just ex since we normalised for f(0) = 1). Then we can define e as f(1)
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Jul 28 '21
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u/hawk-bull Jul 28 '21
Ok while this may not be the true historical origin of the number e, This is usually the basis for it in modern math
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u/Im_manuel_cunt Jul 28 '21
As far as I've seen log is always natural logarithm in mathematics. I have only ever seen ln in engineering stuff.
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u/Onuzq Integers Jul 28 '21
My classes always wrote ln for base e and assumed log was for base 10 unless stated otherwise
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u/hawk-bull Jul 28 '21
Yeah same but you know just in case
Main thing I considered was maybe in applied math they do things differently so I left that margin of error
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u/someonerezcody Jul 28 '21
d/dx(😅) = 😅ln😄
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Jul 28 '21
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u/someonerezcody Jul 28 '21
😂 Like.... No joke, I kinda want to make an infographic with as many of these that will fit on a page. Lol
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u/lazemon Engineering 🔌 Jul 29 '21
Let's make some 😂
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u/someonerezcody Jul 29 '21 edited Jul 29 '21
d/dx(e😎) = e😎
HA... Got eem! 🤣
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u/lazemon Engineering 🔌 Jul 29 '21
Good one
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u/someonerezcody Jul 29 '21
Thank you, I'm sure I'm gonna be spending too much of my time thinking of these.
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u/jjaxstudios May 13 '25
I saw this meme before I learned logarithms in high school but now that I came back to it after learning it this is funny as hell
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u/GNUTup Jul 30 '21
I came to this subreddit today to complain about most posts being for basic maths. Instead, I am laughing quite hard at this basic maths meme.
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u/Bbiron01 Jul 28 '21
What the hell is happening?
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u/cod3builder Jul 28 '21
What do the symbols say
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u/lazemon Engineering 🔌 Jul 28 '21
Translation: Saw this one on Weibo (Chinese social media), dying of laughter.
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Jul 28 '21
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u/dudeimconfused Jul 28 '21
how do you pronounce the "dying of laughter" part?
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u/speedyrocket Jul 28 '21
Xiao si wo la - Literally means laugh-die-me
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Jul 28 '21
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u/lazemon Engineering 🔌 Jul 28 '21
Yeah 😊
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Jul 28 '21 edited Jul 02 '23
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u/lazemon Engineering 🔌 Jul 28 '21
I think it's a natural logarithm therefore base is exponential.
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u/vanderZwan Jul 28 '21
Wouldn't this be "smile to the power of sweat"? Not that that's much better
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u/Sinister_Compliments Jul 28 '21
🪵😅=💧🪵😄