The values of x satisfying the equation |x−1|log3⁡x2−2logx⁡9=(x−1)7 is / are

|x−1|log3⁡x2−2logx⁡9=(x−1)7Since L.H.S. > 0. So, x > 1∴ (x−1)log3⁡x2−2logx⁡9=(x−1)7⇒ x−1=1 or log3⁡x2−2logx⁡9=7⇒ x=2 or 2log3⁡x−41log3⁡x−7=0⇒ x=2 or 2log3⁡x2−7log3⁡x−4=0⇒ x=2 or log3⁡x=−1/2,4⇒ x=2 or x=3−1/2,34⇒ x=2,81