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Solve log(0.2). (x+2)/x le 1....

Solve ` log_(0.2). (x+2)/x le 1`.

A

`(-oo, -5//2] cup (0, oo)`

B

`[5//2, oo)`

C

`(-oo, -2) cup (0, oo)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Note that `"log"_(0.2) ((x+2)/(x))` is meaningful, if
`(x+2)/(x) gt0 rArr x in (-oo, -2) cup (0, oo)`
Now,
`"log"_(0.2) ((x+2)/(x)) le 1`
`rArr (x+2)/(x) ge (0.2)^(-1)`
`rArr (x+2)/(x) ge (1)/(5)`
`rArr (x+2)/(x) - (1)/(5) ge 0`
`rArr (4x + 10)/(5x) ge 0 rArr (2x+5)/(x) ge 0 rArr x in (-oo, -5//2] cup (0, oo)`
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OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Section I - Solved Mcqs
  1. The values of x satisfying x^("log"(5)) gt5 lie in the interval

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  2. The solution set of the equation "log"(x)2 xx "log"(2x)2 = "log"(4x...

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  3. Solve log(0.2). (x+2)/x le 1.

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  4. Solve for x: 5^(log x) + 5x^(log 5) =3 (a>0)

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  5. The number of solutions of "log"("sin"x)(2^(" tan"x)) gt 0 in the inte...

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  6. The set of real values of x for which 2^("log"(sqrt(2))(x-1)) gt x+...

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  7. Find the number of solution to equation log(2)(x+5) = 6 - x:

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  8. The set of values of x for which "log"(e) x gt (x-2)/(x), is

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  9. The number of solutions of the equation 3"log"(3)|-x| = "log"(3) x^(...

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  10. The number of values of x satisfying 1 +"log"(5) (x^(2) + 1) ge "lo...

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  11. The number of ordered pairs (x, y) satisfying 4("log"(2) x^(2))^(2) +...

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  12. The value of (1)/(log(bc)abc)+(1)/(log(ca)abc)+(1)/(log(ab)abc) is equ...

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  13. Complete set of solution of log (1//3) (2 ^(x +2) - 4 ^(x)) ge -2 is :

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  14. The value of e^("log"(e) x+ "log"(sqrt(e)) x+ "log"(root(3)(e)) x +...

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  15. IF x=198! then value of the expression 1/(log2x)+1/(log3x)+...+1/(log1...

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  16. If [.] denotes the greatest integer function, then thevalue of natura...

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  17. The set of real values of x satisfying log(1/2) (x^2-6x+12)>=-2

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  18. If log(0.04) (x-1)>=log(0.2) (x-1) then x belongs to the interval

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  19. If "log"(a) x xx "log"(5)a = "log"(x) 5, a ne 1, a gt 0, " then "x =

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  20. If log(0.5) sin x=1-log(0.5) cos x, then number of values of x in [-2p...

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