Home
Class 12
MATHS
If a, b, c are distinct positive real nu...

If `a, b, c` are distinct positive real numbers each different from unity such that `(log_b a.log_c a -log_a a) + (log_a b.log_c b-logb_ b) + (log_a c.log_b c - log_c c) = 0,` then prove that `abc = 1.`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If a,b,c are distinct real number different from 1 such that (log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to

If x is a positive real number different from 1 such that log_a x, log_b x, log_c x are in A.P then

Prove that: (log_a(log_ba))/(log_b(log_ab))=-log_ab

1/(1+log_b a+log_b c)+1/(1+log_c a+log_c b)+1/(1+log_a b+log_a c)

If a, b, c are positive real numbers, then the minimum value of a^(logb-logc)+b^(logc-loga)+c^(loga-logb) is

If log_a x, log_b x, log_c x are in A.P then c^2=

If log_b x=p and log_b y=q, then log_b xy=

If a, b, c are positive real numbers, then (1)/("log"_(ab)abc) + (1)/("log"_(bc)abc) + (1)/("log"_(ca)abc) =

Prove that: log_a x=log_bx xx log_c b xx…xx log_n m xx log_a n

If a, b, c are positive real numbers, then a^("log"b-"log"c) xx b^("log"c-"log"a) xx c^("log"a - "log"b)

ALLEN-LOGARITHMS-All Questions
  1. If a^(2) + b^(2) = 7 ab," prove that " log((a+b)/3) = 1/2 (log a + lo...

    Text Solution

    |

  2. If (log)a x=p\ a n d(log)b x^2=q ,\ t h e n(log)xsqrt(a b) is equal to...

    Text Solution

    |

  3. If a, b, c are distinct positive real numbers each different from unit...

    Text Solution

    |

  4. Evaluate: 81^(1//log(s)3) + 27^(log(g)36) + 3^(4//log(l)9)

    Text Solution

    |

  5. If ||x-1|-2|=5 then find xdot

    Text Solution

    |

  6. Solve : x|x+3|+2|x+2|=0

    Text Solution

    |

  7. Show that log4 (18) is an irrational number

    Text Solution

    |

  8. If in a right angled triangle, a\ a n d\ b are the lengths of sides ...

    Text Solution

    |

  9. Solve for x the following equation 6/5.a^(log xlogg10 aloga 5)-3^(log1...

    Text Solution

    |

  10. The value of expression, (log)4((x^2)/4)-2(log)4(4x^4) when x=-2 is (a...

    Text Solution

    |

  11. Which one of the following denotes the greatest positive proper fra...

    Text Solution

    |

  12. The equation (log)2(2x^2)+(log)2xdotx^((log)x((log)2x+1))+1/2log4 2(x^...

    Text Solution

    |

  13. Given system of simultaneous equations 2^x\ . 5^y=1\ a n d\ 5^(x+1). 2...

    Text Solution

    |

  14. If (log)c 2.(log)b 625=(log)(10)16.(log)c 10\ w h e r e\ c >0; c!=1; b...

    Text Solution

    |

  15. Number of ciphers after decimal before a significant figure comes i...

    Text Solution

    |

  16. Which of the following when simplified reduces to an integer? a.(2l...

    Text Solution

    |

  17. The equation ((log)8(8/(x^2)))/(((log)8x^2))=3 has- a.\ no integra...

    Text Solution

    |

  18. Which of the following when simplified, vanishes? a.1/((log)3 2)+2/((...

    Text Solution

    |

  19. The number N=(1+2log(3)2)/((1+log(3)2)^(2))+(log(6)2)^(2) when simplif...

    Text Solution

    |

  20. Which of the following are correct? a.(log)3 19.(log)(1//7)3.(log)4 1...

    Text Solution

    |