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The least value of the expression 2(log)...

The least value of the expression `2(log)_(10)x-(log)_x(0, 01)dot` for `x >1,` is 10 (b) 2 (c) `-0. 01` (d) 4

A

1

B

2

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`2"log"_(10)x -"log"_(x) 0.01`
`=2 "log"_(10)x - "log"_(x) (10)^(-2)`
` =2 "log"_(10) x + 2"log"_(x) 10`
`=2("log"_(10)x + (1)/("log"_(10)x)) ge 2 xx 2 = 4 " " [because x gt 1 therefore "log"_(10)x gt 0]`
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