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.
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