I know, that showing:
Let y = ln(x) shows us by definition that e^y = x, ∴ e^ln(x) = e^y = x
This is simple and is correct, but I don't get an "intuitive sense" for a logarithm and how it really "undoes" exponentiation, I'm not really sure how to express what I don't know other than "I just dont feel it" but could someone explain to me step by step or a video to really get an intuitive sense?
Thanks & God bless
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>>>/sqt/
What? I don't get the joke.
Because it's the inverse function
function(inverse(whatever)))=whatever
we have /sqt/, silly question threads :)
In simple terms, imagine a function that makes X go 2 units up
the inverse makes X go 2 units down
if you apply both, you end up with X
well, same is true for e^ln(x)=x, except e^x and ln(x) are a bit more complex than that
>God bless
End your life
edgy, the greatest scientists were Christian
It's because for every real number x, e^x has a single image in the positive real numbers. So for every number y in the positive real numbers you can find a number x in the reals that has the property e^x = y.
You then call x the natural logarithm of y. So it's defined as the inverse of e^x. The properties of ln then can be found out by the properties of e^x. To simplify it. Tl;dr it's defined this way.
I guess this can be found in any analysis 1 book
damn, guess that means Einstein, Dirac, Shrodinger, Richard Feynamm etc. aren't among the greatest scientists
>End your life
>>>/reddit/ is that way, don't let the door hit ya where the priest fucked ya
Correct
Their identifying as such might be related to the fact that for thousands of years we ostracized or imprisoned heretics. Also, many modern scientists sympathize with an idea of God that is decidedly not Christian, but Christians mix and match their words to label them as fellow examples of Christians.
I'm not him, and I'm not offended by your existence, but fuck off with that generalization of "the greatest scientists".
I am sure Newton was just pretending :^)
But does that also mean ln(e(whatever)) = whatever? I suppose it does and seems logical. I think something may have just clicked, I was thinking about "all possible ways in which I can apply ln on e or e on ln and thought that somehow the order mattered
Oh I forgot to check the catalog sorry
So it doesnt matter in any possible way how I apply ln on e or e on ln right? i'll eventually get the original thing back out
Oh I see
I meant this as a figure of speech, something like a good note to leave on after requesting something, not as in I literally hope a mysterious bearded man from the sky blesses you
Y'all motherfuckers need Cauchy
Strict Catholic renewed mathematics
Some of the most astonishing results in analysis as far as I can tell.
>ln(e(whatever)) = whatever
That's correct
the greatest scientists were shit m8
>Their identifying as such might be related to the fact that for thousands of years we ostracized or imprisoned heretics
People who seriously believe that are too young to post on this site
I did not mean to imply no great scientist has ever been Christian you dolt :^)
:)
>But does that also mean ln(e(whatever)) = whatever?
That's what ln(e(x)) =x means, yes. Variables are just, "I'm naming this whatever thing so I can use it in multiple places"
Assuming no restrictions are stated, it can be anything.
Remember PEMDAS?
Focus on evaluating the exponent first....
The term "ln(x)" is essentially asking...
"e to the power of what number makes it equal to x?"
So, once you evaluate the expression you get a number that once e is powered by it equals x.
okay so the next part of the equation says, take that number you get and then power e to it and what do you get. Clearly is has to be x.
There you go, you've simplified the formula without knowing the actual variable's value because you unfolded the logic described by the formula and saw that it canceled out (and hence simplified) a redundant statement.
Here is an analogous problem that doesn't use powers to demonstrate what happened in a simpler plane of thought.
Take the relation:
X*(1/X) = X
This one is probably too intuitive to see how the logic play out but hopefully you get the point.
Now that I have taught you math, how about you teach me how to get girls?
