If (x+1)log10⁡(x+1)=100(x+1) then

(x+1)log10⁡(x+1)=100(x+1)⇒ log10⁡(x+1)log10⁡(x+1)=log10⁡(100(x+1))⇒ log10⁡(x+1)log10⁡(x+1)=2+log10⁡(x+1) Let  log10⁡(x+1)=y⇒ y2−y−2=0⇒ y=2 or −1⇒ log10⁡(x+1)=2,−1⇒ x+1=100,1/10⇒ x=99 or −9/10