Question

ln(x-2)<0 if and only if:

Answer 1

Hmmm, since \(e^x\) is a one to one function, so I think you can use \(e^x\) on both sides..

\[
e^{\ln (x-2)} < e^0\\
x-2 < 1
\]

Answer 2

Inequalities are a bit tricky because you have to be aware of things like sign changes.

Answer 3

so x<3 ?

Answer 4

Since \(e^x\) is always increasing, then this should maintain equality.

Answer 5

Yes, but it might also be important to consider the domain of \(\ln(x)\) as well

Answer 6

It not defined for non-positive numbers. That's why you need \(0<x-2\)

Answer 7

aahh i see so its 2<x<3 correct?

Answer 8

That looks right.