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Natural logs test problem

  1. Sep 4, 2006 #1
    hey
    2day i had a test in intro calc and was given the following problem to solve:

    [tex]50e^(2x) = 100e^(0.5x)[/tex]

    i was quite annoyed :mad: at this problem because i didn’t know how to solve it. although i do know that natural logs need to be taken on both sides to solve it, however the coefficient of the e really had me confused. any help would be greatly appreciated, thanks,
    Pavadrin
     
  2. jcsd
  3. Sep 4, 2006 #2

    J77

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    What happens if you multiply both sides by exp(-0.5x)... ?
     
  4. Sep 4, 2006 #3

    danago

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    Gold Member

    I got stuck on the same question :(

    heres the working i did for it after the test.

    [​IMG]
     
  5. Sep 4, 2006 #4
    if both sides are multiplied by exp(-0.5x) would that make it:

    [tex]50e^2.5x = 100e^x[/tex]

    but i don't see how that helps, thanks for the relpy though
     
  6. Sep 4, 2006 #5

    Astronuc

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    Staff: Mentor

    eax * e-ax = eax-ax = e0 = 1

    danago is correct.

    Using ln,

    [tex]50e^{2x} = 100e^{0.5x}[/tex]

    start by dividing the equation by 50

    [tex]e^{2x} = 2e^{0.5x}[/tex]

    take natural log

    [tex]2x = ln 2\,+\,0.5x[/tex]

    [tex]1.5x = ln 2[/tex]

    [tex]x = \frac{ln 2}{1.5}[/tex]
     
    Last edited: Sep 4, 2006
  7. Sep 4, 2006 #6

    J77

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    I just didn't want to give the game away :smile:
     
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