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Math Help - I dont really understand this logarithmic rule...

  1. #1
    Senior Member
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    I dont really understand this logarithmic rule...

    question number 1:
    a ^ (log x to the base a) = x
    or

    10 ^ (log x) = x

    or

    e ^ (lnx) = x

    can u please help me understand these three?

    question number 2:
    confused about the ln problem help!!!
    Find x
    ln5 + ln10 = lnx

    kindly pls help me understand the two questions we have a test tommorow and i need to get perfect
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    question number 1:
    a ^ (log x to the base a) = x
    or

    10 ^ (log x) = x

    or

    e ^ (lnx) = x

    can u please help me understand these three?

    question number 2:
    confused about the ln problem help!!!
    Find x
    ln5 + ln10 = lnx

    kindly pls help me understand the two questions we have a test tommorow and i need to get perfect
    The answer to your first problem is that a^ and "log to the base a" are inverse functions. So a^{log(a)x} = x and log(a)a^x = x by definition.

    ln(5) + ln(10) = ln(x)

    The sum of two logs multiplies the arguments, ie ln(a) + ln(b) = ln(ab), so

    ln(5*10) = ln(x)

    ln(50) = ln(x)

    Thus x = 50.

    -Dan
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  3. #3
    MHF Contributor Quick's Avatar
    Joined
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    New England
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post

    question number 2:
    confused about the ln problem help!!!
    Find x
    ln5 + ln10 = lnx

    kindly pls help me understand the two questions we have a test tommorow and i need to get perfect
    Rules of logs:

    log(x^y)=y*log(x)

    and

    log(xy)=log(x)+log(y)

    therefore: ln5+ln10=ln(5*10)=ln50

    so x equals 50.
    Last edited by Quick; September 26th 2006 at 12:48 PM. Reason: basic mistake
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