Home
Class 12
MATHS
The x , y , z are positive real numbers ...

The `x , y , z` are positive real numbers such that `(log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3,` then the value of `(1/(2z))` is ............

Text Solution

Verified by Experts

The correct Answer is:
5
` z = 8x^(3), z = 5^(6)y^(6), z = x^(2//3) y^(2//3)`
` rArr x = (z^(1//3))/2, y = (z^(1//6))/5`
` rArr z = 1/(2^(2//3)) z^(2//9) * (z^(2//18))/(5^(2//3))`
` rArr z^(2//3) = 1/((10)^(2//3)) or z = 1/(10)`
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

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .

If x,y,z are positive real numbers such that x^(2)+y^(2)+Z^(2)=7 and xy+yz+xz=4 then the minimum value of xy is

If x+y+z=5 and x y+y z+z x=3 , then the greatest value of (x) is

If (log_2x)/4=(log_2y)/6=(log_2z)/(3k) and x^3 y^2 z=1 , then k is equal to

Given that x ,y ,z are positive real such that x y z=32. If the minimum value of x^2+4x y+4y^2+2z^2 is equal m , then the value of m//16 is.

If x ,y ,a n dz are positive real umbers and x=(12-y z)/(y+z) . The maximum value of x y z equals.

If x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a ,prove that 1+x y z=2y z

If (log)_2y=xa n d(log)_3z=x , find 72^x in terms of yand zdot

If ("log"x)/(y - z) = ("log" y)/(z - x) = ("log" z)/(x - y) , then prove that xyz = 1.

If x gt 1, y gt 1, z gt 1 are in G.P then 1/(1 + log x),1/(1 + log y),1/(1 + log z) are in

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

    |