The roots of the equation 2x+227xx-1=9 are given by

2x+2.33x/(x-1)=9 taking log, we get(x+2) log 2+(3xx-1)log 3=2 log 3 ⇒(x+2)(log 2+1x-1log 3)=0 ⇒x=-2 or 11-x=log 2log 3 ⇒1-x=log 3log 2⇒x=1-log 3log 2