Home
Class 11
MATHS
If log0.3(x-1)ltlog0.09(x-1), then x lie...

If `log_0.3(x-1)ltlog_0.09(x-1)`, then x lies in the interval

A

`(2, oo)`

B

`-2, -1`

C

`(1, 2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`"log"_(0.3) (x-1) lt "log"_(0.09) (x-1)`
Clearly, it is defined for ` x gt 1`
Now,
`"log"_(0.3)(x-1) lt "log"_(0.09) (x-1)`
`rArr "log"_(0.3)(x-1) lt "log"_((0.3))^(2) (x-1)`
`rArr "log"_(0.3)(x-1) lt (1)/(2) "log"_(0.3) (x-1)`
`rArr "log"_(0.3)(x-1) lt 0 rArr x -1 gt (0.3)^(0) rArr x gt 2 rArr x in (2, oo)`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|66 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • INEQUALITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise EXERCISE SECTION-II (Assertion-Reason )|1 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If (log)_(0. 3)(x-1)<(log)_(0. 09)(x-1), then x lies in the interval (2,oo) (b) (1,2) (-2,-1) (d) None of these

If log_(0.5)(x-2)ltlog_(0.25)(x-2) then x lies is the interval (A) (-3,-2) (B) (2,3) (C) (3,oo) (D) none of these

If log_(0.3) (x - 1) lt log_(0.09) (x - 1) , then x lies in the interval

(|x|-1)/(|x|-2) <= 0 then x lies in the interval

If log_(0.04) (x-1)>=log_(0.2) (x-1) then x belongs to the interval

If a!=0 and log_x (a^2+1)lt0 then x lies in the interval (A) (0,oo) (B) (0,1) (C) (0,a) (D) none of these

If "log"_(4)(3x^(2) +11x) gt 1 , then x lies in the interval

If log_(2)(x-2)ltlog_(4)(x-2) ,, find the interval in which x lies.

If 3x^(2)+4kx+1 gt 0 for all real values of x, then k lies in the interval

The value of the definite integral int_0^1(x\ dx)/ (x^3+16) lies in the interval [a,b]. Then smallest such interval is

OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Section I - Solved Mcqs
  1. Solve log(2)|4-5x| gt 2.

    Text Solution

    |

  2. The sum of the series "log"(4)2-"log"(8)2 + "log"(16)2- "log"(32) 2...

    Text Solution

    |

  3. If log0.3(x-1)ltlog0.09(x-1), then x lies in the interval

    Text Solution

    |

  4. The values of x satisfying x^("log"(5)) gt5 lie in the interval

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |