IIT-JEE 1980Question 1
The least value of the expression $2\log_{10}x-\log_{x}(0.01)$, for $x>1$, is
Sets, Relations and Function
Solution
With $t=\log_{10}x>0$: $2t-\log_x0.01=2t+\frac2t\ge4$ by AM-GM, equality at $t=1$. Least value $4$, not listed.