1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Solving a logarithmic equation

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    I've reviewed my logarithmic rules, but I cannot get to the right solution. I should be trying to get one e^x on each side so that I can take the ln of both sides and end up with a simple algebraic process to solve.

    3. The attempt at a solution
    This is as far as I get without running into my problem:

    I guess here I could take the ln of both sides, but I guess I'm confused about what happens to the x^2, and to the 5.


    Ahh, Thanks for the reminder. Don't wanna bump this any more.

    Took ln of both sides, ended with:



    Is that the correct way to that solution?
    Last edited: Apr 24, 2009
  2. jcsd
  3. Apr 24, 2009 #2
    Remember your exponent and logarithm rules (they're pretty similar): If a, b, and c are real numbers, then:
    (ab)c = abc
    ln(a) + ln(b) = ln(ab).
    The latter is derived from the fact that eaeb = ea+b.
  4. Apr 25, 2009 #3
    Indeed. You can check it by replacing x with ln(5) in the original equation. Since both sides are positive (the natural logarithm has only a positive domain), it is also the only real solution.
  5. Apr 26, 2009 #4


    User Avatar
    Science Advisor

    If you let y= ex, then your equation is y2- 5y= y(y- 5)= 0. Can you solve that?

    ?? There is NO x^2. There is (e^x)^2.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook