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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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

if a ,b ,c are in G.P.,then (log)_a 10 ,(log)_b10,(log)_c 10 are in____

(lim)_(x->oo)a^xsin(b/(a^x)),\ a , b >1 is equal to a. b b . a c. a(log)_e b d. b(log)_e a

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 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)_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 (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 a ,\ b ,\ c are in G.P. prove that 1/((log)_a m),1/((log)_b m),1/((log)_c m) are in A.P.

If (log)_a b=2,(log)_b c=2a n dlog_3c=(log)_3a+3,t h e n(a+b+c) is equal to 93 b. 102 c. 90 d. 243

If log_a a. log_c a +log_c b. log_a b + log_a c. log_b c=3 (where a, b, c are different positive real nu then find the value of a bc.

ALLEN-LOGARITHMS-All Questions
  1. lf logpq+logq r +logr p vanishes where p, q and r are positive reals d...

    Text Solution

    |

  2. The solution set of the system of equations log12 x(1/(logx 2)+log2 y)...

    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))=1/2then find x.

    Text Solution

    |

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

    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 I: the equation (log)(1/(2+|"x"|))(5+x^2)=(log)()(15+sqrt(x)...

    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. Let a^((log)b x)=c\ w h e r e\ a ,\ b ,\ c\ &\ x\ are parameters. O...

    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

    |