Question

Does ln(x^2)-ln(x)=ln(x)

Answer 1

Yes, but it is a little subtle.

If we had just ln(x^2), we would not know if x was strictly positive. Since we have ln(x), we do know that x is strictly positive.

ln(x^2) - ln(x) = ln((x^2)/x) = ln(x)

Answer 2

u can write ln(x^2) in this form:
ln(x^2)=2ln(x)
so 2 ln(x)-ln(x)=ln(x)

Answer 3

\(ln(x^2) = 2ln(x)\) ONLY if \(x > 0\) Always think about the Domain. Always!