/sci/ - Science & Math

>>11272525
that is the definition of the natural logarithm, yes

>>11272525
But that's wrong. What is integral of 1/0?

>>11272554
Shitty bait.

>>11272709
Bait? No.
[eqn] \ln x=\int_1^x\frac{\text{d}t}{t} [/eqn]
is true by definition.
[eqn] \exp x=\sum_{n=0}^\infty\frac{x^n}{n!} [/eqn]
is also true by definition.
Showing that log() is the inverse of exp() requires a proof, however. Proving that the derivative of exp(x) wrt x is equal to exp(x) is trivial provided the definition above.

yo you guys are retarded and cant even grasp the basic shit required

>>11272525
correction: log|x|

>>11272722
Trying to sound smart and being better at [math]\rm\LaTeX[/math] won't make your shitty bait any more convincing.

>>11272926
whats wrong?

>>11272525
well this has convinced me that /sci is truly on a whole entirely different level than the rest of humanity. Only Einstein level geniuses could possibly deduce something so unimaginably complex as this. I am in awe and my brain is trembling from the sheer complexity of this unfathomable idea. Even comprehending how one might even begin the process of stating to contemplate the basis for how something like this might even exist will certainly elude the rest of humanity for millennia at the very least, assuming humanity as a whole can one day evolve to match the unparalleled IQ of even one of the geniuses on this board. Truly godlike how some being could posses this much power in their incredible intellect.

>>11272525
You can define most inverse functions by integrals

>>11272700
log(0)

>>11272722
Not him, but you sound fucking autistic if you think these functions have universal agreed upon definitions. You could start with exp with any of the equivalent definitions and show that on some domain the inverse exist. and define ln as such and you would get all the properties you want. Then it's not that hard to show the derivative of ln(x) is 1/x by the inverse function theorem.

>>11272554
>>11272722
Why is an integral definition better than a definition as an inverse?

>>11273619
This

>>11273709
because defining it as an integral contains more information. We are connecting log to 1/x, which is something you might not expect just from defining it as the inverse of the exp function.

>>11273738
Lmao it doesn't give you more information at all, it just gives you different information (relation to 1/x vs. relation to exp)

>>11273751
I suppose it would be the same information, since the definitions can be proven from each other.

>>11273466
Undefined. Divergent.

>>11272722
>is true by definition.

>>11273709
>Why is an integral definition better than a definition as an inverse?
Easier to evaluate numerically desu.

no!!!!!!!!!
ln(x) +c

>>11273980
"Yes"