(b) Taking log on both sides [(log‌x)2−3‌log‌x+1]‌log‌x>log‌103 (log‌x)3−3(log‌x)2+log‌x−3>0 (log‌x)2[log‌x−3]+1[log‌x−3]>0 (log‌x−3)[(log‌x)2+1]>0 log‌x−3>0 ⇒log‌x>3 ⇒log‌x>log‌1000 ⇒x>1000 ∴ (1000 < S < ∞) is the correct answer.