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- Sep 24th 2009, 04:05 PM #1

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- Sep 24th 2009, 04:07 PM #2

- Sep 25th 2009, 04:16 AM #3

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- Sep 25th 2009, 05:18 AM #4
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