Home
Class 12
MATHS
The value of 6+ log(3//2) (1/(3sqrt2)...

The value of
` 6+ log_(3//2) (1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)...))))` is ________.

Text Solution

Verified by Experts

The correct Answer is:
4
Let ` sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)...)))= y`
So, ` 4-1/(3sqrt2)y=y^(2)" "(y gt 0)`
` or y^(2)+1/(3sqrt2)y-4 = 0`
` or y = 8/(3sqrt2)`
So, the required value is
` 6+log_(3//2)(1/(3sqrt2)xx8/(3sqrt2))=6 + log_(3/2). 4/9= 6 - 2 = 4`.
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise JEE MAIN|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise JEE ADVANCED|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Matrix Match Type|3 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

The value of 6+(log)_(3/2)[1/(3sqrt(2)) * sqrt{ (4 - 1/(3sqrt(2))) sqrt(4 - 1/(3sqrt(2))....... } is ...............

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

Simplify : (sqrt5+sqrt3)((3sqrt3)/(sqrt5+sqrt2)-sqrt5/(sqrt3+sqrt2))

Simplify : 1/(sqrt2+sqrt3)-(sqrt3+1)/(2+sqrt3)+(sqrt2+1)/(3+2sqrt2)

Simplify: 1/sqrt(11-2sqrt(30))-3/(sqrt7-2sqrt(10))-4/(sqrt(8+4sqrt3))

The value of lim_(xto2) (sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

int (dx)/(sqrt(1+sqrt(x)))=(4)/(3)(sqrt(x)-2)sqrt(1+sqrt(x))+c

The value of ((1+sqrt(-3))/2)^6+((1-sqrt(-3))/2)^9 is

Simplify : (3sqrt2)/(sqrt3 +sqrt6) -(4sqrt3)/(sqrt6 +sqrt2) +sqrt6/(sqrt2 +sqrt3)

The value of 5^((log)_(1/5)(1/2))+(log)_(sqrt(2))4/(sqrt(7)+sqrt(3))+(log)_(1/2)1/(10+2sqrt(21)) is.........

CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Numerical Value Type
  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+logx 16=(log)...

    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 integral values of x satisfying the inequality 3^((5/2)log3(12-...

    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. The value of x satisfying x+log10(1+2^x)=x log10 5+log10 6 is

    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

    |

  19. The value of 6+ log(3//2) (1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sq...

    Text Solution

    |

  20. The value of ((log(2)9)^(2))^(1/(log(2)(log(2)9)))xx(sqrt7)^(1/(log(4...

    Text Solution

    |