I recently need to solve the following equation:
$e^{\frac{-A_1^2}{2c^2}}+1>e^{\frac{-A_2^2}{2c^2}}$
where $A_1=ln(K_3/K_1), A_2=ln(K_3/K_2)$ They are actually strike prices (in finance) so $K_1<K_2<K_3$, and c is a positive constant term
What condition can make the inequality correct?
I have really no idea as I cannot take log, and I am not sure how to use derivative to solve them But there is a hint to consider concavity with this equation.