alg 2.

Why is ln(e^-2) = -2.
Why doesn't it = e^-2??

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asked by Miley
  1. ln (e^x) = x ln e = x * 1 = x

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    posted by Damon
  2. so what if it was ln5(e^-2). would the answer be -10?? thanks for your help:)

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    posted by Miley
  3. No, it is only because ln is base e that ln(e^x) = x

    in general
    loga (a^x) = x loga(a) = x*1 = x

    log 5 of 5 is 1, but log5 (e) is not one

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    posted by Damon
  4. okay thanks

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    posted by Miley
  5. it is all because
    b^logb (x) = x
    so
    5^log5 (5) = 5
    so log5 (5) has to be 1

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    posted by Damon
  6. thanks damon!!!!!!

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    posted by Miley

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