Home
Class 11
MATHS
If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)...

If `x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a ,p rov et h a t1+x y z=2y zdot`

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

  • PERMUTATIONS AND COMBINATIONS

    CENGAGE ENGLISH|Exercise All Questions|444 Videos

Similar Questions

Explore conceptually related problems

If x=log_(2a) a,y=log_(3a) 2a and z=log_(4a) 3a then prove that xyz+1=2yz

If x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ then prove that x y z=x y+y z+z xdot

If (log x)/(y-z)=(logy)/(z-x) =(logz)/(x-y) , then prove that: x^x y^y z^z=1

If "log"_(y) x = "log"_(z)y = "log"_(x)z , then

if x =log_a (bc), y= log_b (ca) and z=log_c(ab) then 1/(x+1)+1/(y+1)+1/(z+1)

If log_(2)(x + y) = log_(3)(x - y) = (log 25)/(log 0.2) , find the values of x and y.

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 ............

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 ............

If (log)_3y=xa n d(log)_2z=x , find 72^x in terms of yand zdot

If y=a^(1/(1-(log)_a x)) and z=a^(1/(1-(log)_a y)) ,then prove that x=a^(1/(1-(log)_a z))

CENGAGE ENGLISH-LOGARITHM-All Questions
  1. If P is the number of natural numbers whose logarithms to the base 10 ...

    Text Solution

    |

  2. Find the compound interest on Rs. 12000 for 10 years at the rate of 12...

    Text Solution

    |

  3. If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)(4a)3a ,p rov et h a t1+x y z=...

    Text Solution

    |

  4. Let L denote antilog32 0.6 and M denote the number of positive integer...

    Text Solution

    |

  5. Let x=(0. 15)^(20)dot Find the characteristic and mantissa of the loga...

    Text Solution

    |

  6. Using logarithms, find the value of 6.45 x 981.4

    Text Solution

    |

  7. In the 2001 census, the population of India was found to be 8. 7x10^7d...

    Text Solution

    |

  8. If (log)(10)2=0. 30103 ,(log)(10)3=0. 47712 , then find the number of...

    Text Solution

    |

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

    Text Solution

    |

  10. Solve the equations for x and y:(3x)^(log3)=(4y)^(log 4), 4 ^(log x) ...

    Text Solution

    |

  11. If (log)k xdot(log)5k=(log)x5,k!=1,k >0, then x is equal to k (b) 1/5...

    Text Solution

    |

  12. If p , q in N satisfy the equation x^sqrt(x)=(sqrt(x))^x, then p a n ...

    Text Solution

    |

  13. Solution set of the inequality (log)(0. 8)((log)6(x^2+x)/(x+4))<0 is

    Text Solution

    |

  14. Which of the following is not the solution of (log)3(x^2-2)<(log)3(3/2...

    Text Solution

    |

  15. The true solution set of inequality (log)((x+1))(x^2-4)>1 is equal to ...

    Text Solution

    |

  16. Solve the following equation of x :2(log)x a+(log)(a x)a+3(log)(a^2x)a...

    Text Solution

    |

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

    Text Solution

    |

  18. Which of the following, when simplified, reduces to unity? (a) (log)(...

    Text Solution

    |

  19. If (log)a x=b for permissible values of a and x , then identify the ...

    Text Solution

    |

  20. The number of positive integers satisfying x+(log)(10)(2^x+1)=x(log)(1...

    Text Solution

    |