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If I have a function: y=K*e^x is there a way to rewrite it as y=C*A^x where A does not equal e?
 one year ago
 one year ago
If I have a function: y=K*e^x is there a way to rewrite it as y=C*A^x where A does not equal e?
 one year ago
 one year ago

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experimentXBest ResponseYou've already chosen the best response.1
let, A^i = e i = 1/lnA
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
it will be the same nevertheless, however I am not sure about K and C
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
I´m just wondering if e is such a magical number to appear here and there or if its artificial and we could use a different set of numbers to express the same thing/physical law.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i think e is quite an special number < especially when rate of change depends on initial value. also it has some special property (base of natural log), i think it is best to leave things with e's
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
also stretching or compressing exponential function gives e at some point
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
Hmmm what is so special about e? I only know that the derivative of e^x is again e^x which is quite nice and that I can rewrite e^(ix) in terms of sine and cosine but is there even more to e?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
LOL ... not really sure!!
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
xD I thought there might be some additional stuff I might not know about.^^
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
Medals 0 You can do it by writing e as a^(1/ln(a)) and apply exponential identities but why would you want to? e is such a nice number :)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
e's the best ... LOL
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
From a practical point of view, if you need to differentiate or integrate your function down the road, would you rather deal with e^x or A^x?
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
@beginnersmind I was wondering if the appearance of e in some laws of physics was because somewhat had the hearts for e or because there is no other way to state that law. Might have been just some physicist who loved e and we could rewrite some laws. Ok than I guess e really is that great. :)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
comes naturally from \( \int 1/x dx \)
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
f I integrate or differentiate I am always happy to encounter e ;) But if I just add and multiply I could live without e ;) So it depends on the field.
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
well, a lot of laws are actually of the form e^Cx, so I'm not sure e is especially preferred by nature in those cases. It seems to be notational .
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
So I could easily rewrite y=K*e^(Cx) with some other base?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i've usually encountered in decay equation and distribution function. decay equation < dN/dt = N < depends on initial value distribution function > didn't understand
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
I started wondering while looking at the decay equation like 10 Minutes ago.^^
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
@experimentX in the decay function the choice of the base is somewhat arbitrary. Say you have f(t)=e^(Ct). You could just as easily write f(t)2^(Kt), with a different constant.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
why ... we choose it as natural base for log while integrating < must be some reason.
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
I'm saying e^(Ct) and 2^(Ct/ln2) are the same function. They take the same values.
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
2^(Ct/ln2) that is
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
But If you rewrite it using the ln than e is still in there (in that function). So you can rewrite in a way that you can not see e but it is hidden in the ln.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
we could use the same logic everywhere, the point is why e so that there is no logs on the power?? 1/ ln 2 ??
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
Well, there's a constant, which is an experimentally determined number. When you use e as the base the constant is C. When you use 2 it's K=C/ln2. If you actually measure halflife you're measuring K, so ln2 isn't really "hidden" there.
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
Ops right. ln2 is just some number  there is not an e hidden. So we could really rewrite equations that fit that pattern.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
not really sure if i am understanding ..:(
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
@experimentX Which part? You wrote the same thing as beginnersmind with the rewriting 1/lnA or now 1/ln2.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
e^x/nothing < why nothing in this case?? must be some special property of e A^x/lnA
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
Why e^x/nothing? Who wrote that where?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
usually equation comes that way when we integrate 1/x dx Oo, i think i need to review decay equation, since i ignored \( \lamda \) factor completely.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
LOL ... seems like only e is nice to deal with,
 one year ago

TomLikesPhysicsBest ResponseYou've already chosen the best response.1
:) I guess than everything is alright. What a nice and interesting discussion. If you follow mathematics and physics in class it seems that e is mysteriously everywhere but apparently it is that way because some people are secretly working for e and we could write it in a different way. :) Nevertheless e is a great number for calculus.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yeah ... that i agree!! makes nice, easy and clean.
 one year ago

beginnersmindBest ResponseYou've already chosen the best response.1
To be fair, there are situations where e appears in its own right. E.g. you can't rewrite e^i*pi=1 with any number. (I think)
 one year ago
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