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5e^(7x) = 7e^(10x) ?

  1. Sep 14, 2011 #1
    5e^(7x) = 7e^(10x) ??

    7x ln(5e) = 10x ln(7e)

    7x * (ln5 + ln e) = 10x * (ln7 + ln e)

    7x * (ln5) = 10x * (ln7)

    Now I have nowhere to go. What am I doing wrong?
     
  2. jcsd
  3. Sep 14, 2011 #2

    Dick

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    Re: 5e^(7x) = 7e^(10x) ??

    5e^(7x) probably means 5*(e^(7x)) not (5e)^(7x) as you are treating it.
     
  4. Sep 14, 2011 #3
    Re: 5e^(7x) = 7e^(10x) ??

    How does that make a difference?
     
  5. Sep 14, 2011 #4

    Dick

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    Re: 5e^(7x) = 7e^(10x) ??

    All the difference in the world. Try it.
     
  6. Sep 14, 2011 #5
    Re: 5e^(7x) = 7e^(10x) ??

    5*7x ln e = 7 * 10 ln e

    35x = 70x?

    This doesn't seem right. Can you please explain how I would start this? Is the 5 included in the natural log?
     
  7. Sep 14, 2011 #6

    Dick

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    Re: 5e^(7x) = 7e^(10x) ??

    ln(5*e^(7x))=ln(5)+ln(e^(7x)). It's looking different already, isn't it? Not the same as ln((5e)^(7x))=7x*ln(5e).
     
  8. Sep 14, 2011 #7
    Re: 5e^(7x) = 7e^(10x) ??

    Thank you!
     
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