1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Exponential proof

  1. Feb 7, 2017 #1
    1. The problem statement, all variables and given/known data
    they say 1. ##e^{ln x}= x ## and 2.##e^-{ln(x+1)}= \frac 1 {x+1}## how can we prove this ##e^{ln x}= x ## and also ##e^-{ln(x+1)}= \frac 1 {x+1}##?

    2. Relevant equations


    3. The attempt at a solution
    let ## ln x = a## then
    ##e^a= x,
    ## a ln e= x,##
    →a= x, where
    ## ln x= x
     
    Last edited: Feb 7, 2017
  2. jcsd
  3. Feb 7, 2017 #2
    Set ##y=ln(x+1)## so we ll have that ##e^y=x+1##.
     
  4. Feb 7, 2017 #3
    Delta what are you doing???????????????:smile: so?
     
  5. Feb 7, 2017 #4
    Sorry I now see you have edited the original post.

    It is from the definition of the natural logarithm ##lnx## that ##e^{lnx}=x##. So not much to prove here, it follows directly from the definition.

    Now we want to look at ##e^{-ln(x+1)}##. This is equal to ##\frac{1}{e^{ln(x+1)}}## don't you agree? (it is like saying that ##e^{-y}=\frac{1}{e^y})##
     
    Last edited: Feb 7, 2017
  6. Feb 7, 2017 #5
    Thanks a lot, i was blind but now i see
    let ## ln x = y##............1
    it follows that ## e^y = x##
    taking logs on both sides,
    ## y ln.e = ln x##
    ##y = ln x## now substituting this in original equation 1,
    ##ln x = ln x##,
    implying that ##e^{ln x}= x##
    greetings from Africa, chikhabi
     
  7. Feb 7, 2017 #6
    This is correct but what you doing is like driving in a circle, i.e you start from ##lnx=y## to end up with ##y=lnx## which is essentially the same thing.

    Substituting ##y=lnx## to ##e^y=x## is what proves (if we can call this a mini proof) that ##e^{lnx}=x##.

    Greetings from Athens, Greece.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Exponential proof
  1. Proof for exponentials (Replies: 7)

Loading...