$\text{ The least integral value of }x\text{ satisfying the equation }\mid x^2-1+\log x|=|x^2-1|+|\log x\mid \text{ is }$

$\left|x^2-1+\log x\right|=\left|x^2-1\right|+|\log x|$

$\begin{array}{l}\Rightarrow \left(x^2-1\right)\log x\ge 0\\ \text{ We must have }x>0\\ \Rightarrow x\in (0,\mathrm{\infty })\end{array}$

$\Rightarrow \text{ Least integral value of }x\text{ is }1$