Home
Class 12
MATHS
If a^x=b , b^y=c ,c^z=a and x=(log)b a^...

If `a^x=b , b^y=c ,c^z=a` and `x=(log)_b a^2; y=(log)_c b^3& z=(log)_a c^k ,` where `a,b, c >0` &` a , b , c!=1` then `k` is equal to a.`1/5` b. `1/6` c.`(log)_(64)2` d. `(log)_(32)2`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If x=log_(b)a,y=log_(c)b,z=log_(a)c then xyz=

IF a^x=b,b^y=c,c^z=a,x=(log_ba)^(k1),y=(log_cb)^(k2),z=(log_ac)^(k3) , find the minimum value of 3k_1+6k_2+12k_3 .

If a^(x) = b , b^(y) = c, c^(z) = a, x = log_(b) a^(k_(1)) , y = log_(c)b^(k_(2)), z = log _(a) c^(k_(3)), , then find K_(1) K_(2) K_(3) .

If (a^(log_b x))^2-5 a^(log_b x)+6=0, where a >0, b >0 & a b!=1, then the value of x can be equal to (a) 2^(log_b a) (b) 3^(log_a b) (c) b^(log_a2) (d) a^(log_b3)

If (log)_c 2.(log)_b 625=(log)_(10)16.(log)_c 10 w h e r e c >0; c!=1; b >1; b!=1 determine b- a. 25 b. 5 c. 625 d. 16

If y^(2)=xz and a^(x)=b^(y)=c^(z), then prove that (log)_(a)b=(log)_(b)c

If (log)_b a(log)_c a+(log)_a b(log)_c b+(log)_a c(log)_bc=3 (where a , b , c are different positive real numbers !=1), then find the value of a b c dot

If (1)/(log_(a) x) + (1)/(log_(c) x) = (2)/(log_(b)x ) then a, b, c, are in

ALLEN-LOGARITHMS-All Questions
  1. The solution set of the system of equations log12 x(1/(logx 2)+log2 y)...

    Text Solution

    |

  2. If x1and \ x2 are the solution of the equation x^(3log10^3x-2/3log(10)...

    Text Solution

    |

  3. If a^x=b , b^y=c ,c^z=a and x=(log)b a^2; y=(log)c b^3& z=(log)a c^k ...

    Text Solution

    |

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

    Text Solution

    |

  5. If x^3//4((log)3x)^(2+(log)3x-5//4)=3,\ t h e n\ x has- a. one positiv...

    Text Solution

    |

  6. ((log)(10)(x-3))/((log)(10)(x^2-21))=1/2

    Text Solution

    |

  7. x^((log2 x)+4)=32

    Text Solution

    |

  8. where the base of logarithm is

    Text Solution

    |

  9. 9^(1+logx)-3^(1+logx)-210=0 where the base of log is 10

    Text Solution

    |

  10. Statement 1 is True: Statement 2 is True; Statement 2 is a correct ...

    Text Solution

    |

  11. Statement 1 is True: Statement 2 is True; Statement 2 is a correct ...

    Text Solution

    |

  12. Statement 1 is True: Statement 2 is True; Statement 2 is a correct ...

    Text Solution

    |

  13. Comprehension 1 Let a^((log)b x)=c\ w h e r e\ a ,\ b ,\ c\ &\ x...

    Text Solution

    |

  14. Comprehension 1 Let a^((log)b x)=c\ w h e r e\ a ,\ b ,\ c\ &\ x...

    Text Solution

    |

  15. Comprehension 1 Let a^((log)b x)=c\ w h e r e\ a ,\ b ,\ c\ &\ x...

    Text Solution

    |

  16. Comprehension 2 In comparison of two numbers, logarithm of small...

    Text Solution

    |

  17. Comprehension 2 In comparison of two numbers, logarithm of small...

    Text Solution

    |

  18. Comprehension 3 If P is the non negative characteristic of (log)(10...

    Text Solution

    |

  19. Comprehension 3 If P is the non negative characteristic of (log)(10...

    Text Solution

    |

  20. If (log)(10)33. 8=1. 5289 ,\ t h e n(log)(10)0. 338 is- a. 1 .5289 b....

    Text Solution

    |