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!

Natural Log and e confusion

  1. Aug 6, 2008 #1
    I am starting my first year of college and I reviewing my high school notes from trig pre-cal and there was one thing I couldnt figure out. It was a multiple choice question and I dont have the text book anymore but the answer I circled I cant understand how I arrived to that answer.

    1. The problem statement, all variables and given/known data
    Given that x> 0 and y> 0, simplify e^ln(x) + ln(y)

    3. The attempt at a solution
    What I did was:
    and I circled the answer: X+Y, but I get e^x+y which as an answer. All I wrote was ln and e cancel but I dont understand how they cancel.
  2. jcsd
  3. Aug 6, 2008 #2
    Do you mean e^(ln(x) + ln(y)) ? If that's the case, then you add the two logarithms to get ln(xy) since the arguments are multiplied in log addition. Then using the fact that e^ln(x) = x, you have e^(ln(xy)) = xy. I'm not sure if that answers your question.

    To see why e^ln(x) = x. Remember that ln(x) = log base e of x. Let ln(x) = y. Then converting to exponentiation gives e^y = x, but y = ln(x). Hence e^ln(x) = x.
  4. Aug 6, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    Do you mean e^(ln(x)+ ln(y))? What you wrote is e^(ln(x))+ ln(y).

    No, ln(x)+ ln(y) is not equal to ln(x+ y). As snipez90 said, ln(x)+ ln(y)= ln(xy).
    Then, of course, e^(ln(xy))= xy since e^x and ln(x) are inverse functions.

    Another way to do that is to use the fact that e^(a+b)= e^a e^b:
    e^(ln(x)+ ln(y))= (e^ln(x))(e^ln(y))= (x)(y)= xy.
  5. Aug 7, 2008 #4
    Thanks for the help. I see where I made my mistake now. I was using the wrong log identities, and misunderstand certain things about natural logs.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Natural Log and e confusion
  1. Natural log (Replies: 1)

  2. Natural logs (Replies: 5)