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Solving a logarithmic equation

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data
    (e^x)^2-5(e^x)=0

    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:
    (e^x)^2=5(e^x)

    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.

    Edit:

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

    Took ln of both sides, ended with:

    2x=ln5+x

    x=ln5

    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
    and
    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

    HallsofIvy

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    Staff Emeritus
    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.

     
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