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Math Help - Logarithm help t-t

  1. #1
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    Logarithm help t-t

    1.) 2^(x) = 3 ^(x-1)

    2.) 3^(x+2) = 5^ ( x - 1)
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    2^(x) = 3 ^(x-1)
    2^x = 3^(x+1)

    Take the natural log of both sides (any base will do, actually).

    ln[2^x] = ln[3^(x+1)] <--- log[a^x] = x*log(a) for all bases.

    x*ln(2) = (x+1)*ln(3)

    x*[ln(2) - ln(3)] = ln(3)

    x = ln(3)/[ln(2) - ln(3)] = -ln(3)/[ln(3) - ln(2)]

    (The last step isn't really necessary, I just find it to be a bit tidier since x is negative.)

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    3^(x+2) = 5^ ( x - 1)
    Similar to the first:

    3^(x+2) = 5^(x-1)

    ln[3^(x+2)] = ln[5^(x-1)]

    (x+2)*ln(3) = (x-1)*ln(5)

    x*[ln(3) - ln(5)] = - ln(5) - 2*ln(3)

    x = -[ln(5) + 2*ln(3)]/[ln(3) - ln(5)] = [ln(5) + 2*ln(3)]/[ln(5) - ln(3)]

    -Dan
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  4. #4
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    thanks and gudluk 2 me
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