I want to prove that exp(log(x))=log(exp(x))=x
Now the second one i diff. and get 1/exp(x) * exp(x) = 1
So log(exp(x))= x+ C, Calculation shows c = 0
But hopw do I get the first one
because when i diff. I get exp(log(x))/x , now I have to prove that exp(log(x))=x and so this doesn't help
What can I do now?
yes thanks but,
The problem I had to solve was to prove exp(log(x)=x
So I don't know actually yet, according to the exercise, that this is true
But I know the derivatives of exp and log, and I know there values in 0 and 1. So I use this:
Now if i take the derivative of exp(log(x)), I get exp(log(x))*1/x
This must be equal to 1 then. Then exp(log(x)) must be x, because then
exp(log(x))/x=1, but I can't use this, because this is what I have to prove
Can't I use something else?
so answering your question amounts to proving that the log is the inverse of the exponential function. can you do that?
Further, they define e as the number such that .
From these, the authors develop the usual properties of both Log(x) and exp(x).