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Homework Help: Log problem

  1. Jan 17, 2014 #1
    1. The problem statement, all variables and given/known data
    If y= 10^x, show by taking logarithms to base e that y = exln10

    2. Relevant equations

    3. The attempt at a solution

    Well what I did was y= 10^x so ln y = xln10

    they told me that y = exln10
    so ln y = xln 10 , so ln y = lny

    so y = y
    so y= 10^x.

    The way I did it doesn't feel right to me . Is there another approach?
  2. jcsd
  3. Jan 17, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You seem to have gotten in a loop with this step:

    This is the last meaningful equation you have:

    ln y = x ln 10

    How do you go about getting rid of the logarithms on both sides? That will lead you to your answer.
  4. Jan 17, 2014 #3


    Staff: Mentor

    Now make each side of the equation the exponent on e.
  5. Jan 17, 2014 #4
    you mean do e^y = e^(10^x) ?
  6. Jan 17, 2014 #5
    logca = b is same as writing cb = a . For example log101000 = 3 is equivalent to 103 = 1000 .

    Now use this fact .You are just one step away.
  7. Jan 17, 2014 #6


    Staff: Mentor

    You had ln(y) = xln(10).
    Now write each side as the exponent on e. The idea is that if A = B, then eA = eB.
  8. Jan 18, 2014 #7
    Thank you guys!
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