Solve this inequality $10 > e^{-x}$

Question

Let $x$ be a real number

We want to derive the inequality relationship in terms of $x$ alone:

Method 1: $$10> e^{-x} \implies \ln(10) > -x \implies \ln(10)^2 > x^2 \implies |\ln(10)| > x$$

Method 2: $$10> e^{-x} \implies \ln(10) > -x \implies -\ln(10) < x $$

Which is correct?

Answer 1

Hint: $x>y$ does not imply $x^2>y^2$ (consider $x=1$ and $y=-1$).