Home
Class 12
MATHS
Number of integers satisfying the inequa...

Number of integers satisfying the inequality `(log)_(1/2)|x-3|>-1` is.....

Text Solution

Verified by Experts

The correct Answer is:
2
`log_(1//2)|x-3|gt - 1`
` rArr 0 lt |x-3| lt 2`
` rArr - 2 lt x - 3 lt 2, x ne 3 `
` rArr 1 lt x lt 5, x ne 3`
` :. x in {2, 4}`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise JEE Previous Year|5 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Matrix)|3 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

Number of integers lt=10 satisfying the inequality 2(log)_(1/2)(x-1)lt=1/3-1/((log)_(x^2-x)8) is............

Number of intergers satisfying the inequality x^4- 29x^2+100 le 0 is

The number of integers satisfying the inequality log_(sqrt(0.9))log_(5)(sqrt(x^(2)+5+x))gt 0 is

Number of intergal values of x satisfying the inequality (x^2+6x-7)/(|x+2||x+3|) lt 0 is

Sum of all integral values of x satisfying the inequality (3^((5/2)log(12-3x)))-(3^(log x))>32 is......

The number of integral values of x satisfying the inequality (3/4)^(6x+10-x^2)<(27)/(64)i s________

Sum of integers satisfying sqrt((log)_2x-1)-1/2(log)_2(x^3)+2>0 is......

The smallest integral x satisfying the inequality (1-log_(4)x)/(1+log_(2)x)le (1)/(2)x is.

Let a >2 be a constant. If there are just 18 positive integers satisfying the inequality (x-a)(x-2a)(x-a^2)<0, then find the value of adot

Number of real values of x satisfying the equation log_2(x^2-x)*log_2((x-1)/x)+(log_2x)^2=4 ,is (a) 0 (b) 2 (c) 3 (d) 7

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Numerical)
  1. If log(a)b=2, log(b)c=2, and log(3) c= 3 + log(3) a,then the value of...

    Text Solution

    |

  2. The value of (log(10)2)^3+log(10)8log(10)5+(log(10)5)^3 is ..............

    Text Solution

    |

  3. If (log)4A=(log)6B=(log)9(A+B),t h e n [4(B/A] (where [ ] represents t...

    Text Solution

    |

  4. Integral value of x which satisfies the equation =log6 54+(log)x 16=(l...

    Text Solution

    |

  5. If a = log(245) 175 and b = log(1715) 875, then the value of (1-ab)/...

    Text Solution

    |

  6. The difference of roots of the equation ((log)(27)x^3)^2=(log)(27)x^6 ...

    Text Solution

    |

  7. Sum of all integral values of x satisfying the inequality (3^((5/2)log...

    Text Solution

    |

  8. The least integer greater than (log)2 15 (log)(1/6)2(log)3 1/6 is .......

    Text Solution

    |

  9. The reciprocal of 2/((log)4(2000)^6)+3/((log)5(2000)^6) is ..............

    Text Solution

    |

  10. Sum of integers satisfying sqrt((log)2x-1)-1/2(log)2(x^3)+2>0 is......

    Text Solution

    |

  11. Number of integers satisfying the inequality (log)(1/2)|x-3|>-1 is.......

    Text Solution

    |

  12. Number of integers lt=10 satisfying the inequality 2(log)(1/2)(x-1)lt=...

    Text Solution

    |

  13. The value of (sqrt(3+2sqrt2)+sqrt(3-2sqrt2))^(2^(9)) is .

    Text Solution

    |

  14. The value of 5^((log)(1/5)(1/2))+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(lo...

    Text Solution

    |

  15. The value of N=((log)5 250)/((log)(50)5)-((log)5 10)/((log)(1250)5) is...

    Text Solution

    |

  16. if x+log10 (1+2^x)=xlog10 5+log10 6 then x

    Text Solution

    |

  17. The x , y , z are positive real numbers such that (log)(2x)z=3,(log)(5...

    Text Solution

    |

  18. If a=(log)(12)18 , b=(log)(24)54 , then find the value of a b+5(a-b)do...

    Text Solution

    |