Why does e^ln3 = 3 ??

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I am sure brittanna knows that, but I am sure he did that for the sake of simplicity, given the OP did not understand why e^ln3 = 3

The difference is though is what that brittanna said is mathematically incorrect. What I said is not

Reply 21

stochasticking

Read the above posts for intuition. In a nutshell what you need to know is: e^ln(x) = x
ln(e^x) = x
Plug in x=3.

Reply 22

TeeEm

Original post by ubisoft

Ah fair enough. Can you explain how what the other user said about ln is incorrect? That's how I still think about it too, would like to know if it's wrong.

it does not harm to think powers that is exactly how I have taught it to the huge majority of students.

however e^x = exp(x)

for inverse functions

f^-1f(x) = ff^-1(x) =x (identity function)

by analogy

exp(lnx) = x for all positive x, which we write e^lnx =x
ln(exp(x) = x for all x, which we write ln(e^x) =x

Reply 23

TeeEm

Original post by B_9710

The difference is though is what that brittanna said is mathematically incorrect. What I said is not

I am sorry I hurt your feelings ...
He was incorrect and you were a tiny bit incorrect.

But for both of you I said....
From a teaching point of view, both of you are "correct"

I have often made deliberate decisions to teach mathematical facts incorrectly (to some weak students). This is done to avoid confusion with a "heavy duty" mathematically correct but confusing explanation.

Reply 24

TeeEm

Original post by thecatwithnohat

who even knew drama could arise in the maths forum...about maths :lol:

I do not know how I manage it ....
Every time I get involved into a debate it ends up in an argument ...
There was one last April it lasted over a week, during which 2 people got banned ...
It was me versus someone else which I do not wish to name in the maths courses forum... then you get your supporters fighting with you and the other person's supporters fighting ... I left after 2 days but the fight went on for about a week

Reply 25

stochasticking

Original post by TeeEm

Did you teach A-level TeeEm?

Reply 26

B_9710

Original post by thecatwithnohat

who even knew drama could arise in the maths forum...about maths :lol:

I know

Reply 27

TeeEm

Original post by stochasticking

Did you teach A-level TeeEm?

I only teach a bit from this year because I retired

I teach GCSE, A level exc Decision and high end stats and undergrad methods

(only privately of course)

Reply 28

B_9710

Original post by TeeEm

No one is saying that is wrong. But why give that as an answer when someone just wants a simple explanation. You have to try and make it intuitive really don't you.

Reply 29

stochasticking

Original post by TeeEm

I only teach a bit from this year because I retired

I teach GCSE, A level exc Decision and high end stats and undergrad methods

(only privately of course)

Oh sweet. For undergrad methods, do you teach partials, matrix algebra etc?

Reply 30

TeeEm

Original post by B_9710

No one is saying that is wrong. But why give that as an answer when someone just wants a simple explanation. You have to try and make it intuitive really don't you.

That is exactly what I said not to you but to the chap that correctly or incorrectly called the rest "smug" and your comment sensible.

Maybe it came out the wrong way and your "name" got punished as a result ... I merely said mathematically that is incorrect however from a teaching point of view correct.
I would have given the same explanation like you to a student here...
Many people before you, also said the same as you.
I was annoyed not with your explanation but with that guy's comment calling the rest of us "smug"
scroll back to the start and see for yourself

Reply 31

TeeEm

Original post by stochasticking

Oh sweet. For undergrad methods, do you teach partials, matrix algebra etc?

topics such as those in this index thread
http://www.thestudentroom.co.uk/showthread.php?t=3330283

My site has a lot more questions

Reply 32

B_9710

Original post by TeeEm

Fair enough then. I wouldn't get annoyed about it though, it's only people on TSR

Reply 33

stochasticking

Original post by TeeEm

topics such as those in this index thread
http://www.thestudentroom.co.uk/showthread.php?t=3330283

My site has a lot more questions

Cheers!

Reply 34

davros

Original post by ubisoft

Ah fair enough. Can you explain how what the other user said about ln is incorrect? That's how I still think about it too, would like to know if it's wrong.

I'm sure TeeEm will correct me if I'm wrong but I don't think he was criticising the actual mathematics posted - I think the was criticising the fact that the other poster thought he'd come up with some new way of presenting the argument when in fact all he was doing was saying the same thing as everyone else but in different words!

There are only so many different ways you can say "the definition of an inverse function is one that reverses the effect of the original function" :smile: