If the area of the bounded region R ={(x, y): max {0, log_e x} ≤ y ≤ 2^x, 1/2 ≤ x ≤ 2} is, α( log_e 2)^-1+β( log_e 2)+γ, then the value of (α+β-2…

If the area of the bounded region $\displaystyle \mathrm{R}=\left\{(x, y): \max \left\{0, \log _{\mathrm{e}} x\right\} \leq y \leq 2^x, \frac{1}{2} \leq x \leq 2\right\}$ is, $\displaystyle \alpha\left(\log _{\mathrm{e}} 2\right)^{-1}+\beta\left(\log _{\mathrm{e}} 2\right)+\gamma$, then the value of $\displaystyle (\alpha+\beta-2 \gamma)^2$ is equal to :