1.

The least value of the expression `2(log)_(10)x-(log)_x(0. 01),`for `x >1,`is (1980, 2M)10 (b) 2(c) `-0. 01`(d) None of theseA. 10B. 2C. `-0.01`D. None of these

Answer» Correct Answer - D
Here, `2log_(10)x-log_(x)(10)^((-2))=2log_(10)x+2log_(x)10`
`=2log_(10)x+2(1)/(log_(10)x)=2(log_(10)x+(1)/(log_(10)x)) " ...(i)" `
Using `AM ge GM,` we get
`=(log_(10)x+(1)/(log_(10)x))/(2) ge (log_(10)x(1)/(log_(10)x))^(1//2)`
`rArr log_(10)x+(1)/(log_(10)x) ge 2 " ...(ii)" `
`or 2 log_(10)x-log_(x)(0.01) ge 4`
Hence, least value is 4,


Discussion

No Comment Found

Related InterviewSolutions