[Heir of Ramanujan]

Solution

$2(\ln{10})(\log\left|\,x-2\right|) = \ln{(x^{2}+1)}$
$\ln{10^{2(\log\left|\,x-2\right|)}} = \ln{(x^{2}+1)}$
$10^{\log\left|\,x-2\right|^{2}} = x^{2}+1$
$x^{2}-4x+4 = x^{2}+1$
$-4x = -3$
ดังนั้น $\left|\,4x\right| = 3$