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  1. #1
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    Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ln(a) - ln(b) = ln(a - b) for all positive real numbers a and b.
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  2. #2
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    Quote Originally Posted by Dadillar View Post
    Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ln(a) - ln(b) = ln(a - b) for all positive real numbers a and b.
    try a = e and b = 1
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  3. #3
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    Quote Originally Posted by Dadillar View Post
    Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ln(a) - ln(b) = ln(a - b) for all positive real numbers a and b.

    the statement is false because
    ln(a) - ln(b) = ln(a) + ln (b^-1)
    =ln(a * b^-1)
    = ln(a/b)
    Last edited by ramiee2010; September 25th 2009 at 04:18 AM. Reason: removing extra images which are pasted by mistake
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  4. #4
    Senior Member pacman's Avatar
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    ln(a) - ln(b) = ln(a - b)?
    .
    For all positive real numbers a and b? Maybe for SOME, since it violates the logarithmic rule, ln x - ln y = ln(x/y) not ln (a -b)

    but there are few VALUES where it is true . . . .

    let us try solving it, use this property, ln x - ln y = ln(x/y)

    ln(a/b) = ln (a - b)

    raise both sides to e,

    e^(ln(a/b)) = e^(ln (a - b))

    but e^ln z = z.

    a/b = a - b, cross multiply

    a = ab - b^2

    b^2 - ab + a = 0, well it is quadratic in b

    Discriminant = b^2 - 4ac = (-a)^2 - 4(1)(a) = a^2 - 4a > or = 0, some values will do
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