Home
Class 12
MATHS
If a, b, c are consecutive positive inte...

If a, b, c are consecutive positive integers and log (1+ac) = 2K, then the value of K is

A

log b

B

log a

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` a = x - 1, b = x, c = x+1`
Now `log(1+ac)=log [1+(x-1)(x+1)]`
` = log x^(2) = 2 log x = 2 log b`
` rArr K = log b`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Comprehension)|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.6|6 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 n is a positive integer and (1+i)^(2n)=k cos(n pi/2) , then the value of k is

If the roots of the cubic x ^(3) +ax ^(2) + bx +c=0 are three consecutive positive integers, then the value of (a ^(2))/(b +1) =

If the roots of ht cubic,x^(3)+ax^(2)+bx+c=0 are three consecutive positive integers,then the value of (a^(2)/b+1) is equal to

If a,b,c are any three consecutive integers, prove that log(1+ac)=2log b

If a,b,c are any three consecutive integers, prove that log(1+ac)=2log b

If a b and c are consecutive integers, in that order, what is the value of b? I. b = a+c II. ac =-1

sum_(k=1)^(360)(1)/(k sqrt(k+1)+(k+1)sqrt(k)) is the ratio of two relatively prime positive integers m and n then the value of m+n is equal to

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. If (21. 4)^a=(0. 00214)^b=100 , then the value of 1/a-1/b is

    Text Solution

    |

  2. The value of log ab- log|b|=

    Text Solution

    |

  3. If a, b, c are consecutive positive integers and log (1+ac) = 2K, then...

    Text Solution

    |

  4. if (a+log4 3)/(a+log2 3)= (a+log8 3)/(a+log4 3)=b then find the value ...

    Text Solution

    |

  5. If p >1a n dq >1 are such that log(p+q)=logp+logq , then the value of ...

    Text Solution

    |

  6. The value of (1+2(log3 2)/((1+(log)3 2)^2)+((log)6 2)^2 is 2 (b) 3 (...

    Text Solution

    |

  7. If (log)4 5=aa n d(log)5 6=b , then (log)3 2 is equal to 1/(2a+1) (b)...

    Text Solution

    |

  8. If log(10) 2 = a, log(10)3 = b" then "log(0.72)(9.6) in terms of a an...

    Text Solution

    |

  9. There exists a natural number N which is 50 times its own logarithm to...

    Text Solution

    |

  10. The value of ((log)2 24)/((log)(96)2)-((log)2 192)/((log)(12)2) is

    Text Solution

    |

  11. log(x-1)x*log(x-2)(x-1)*...*log(x-12)(x-11) = 2,x is equal to

    Text Solution

    |

  12. If f.(x)= log((1+x)/(1-x)), then

    Text Solution

    |

  13. If a^4b^5=1 then the value of loga(a^5b^4) equals

    Text Solution

    |

  14. The value of 3^((log)4 5)-5^((log)4 3) is 0 (b) 1 (c) 2 (d) none of...

    Text Solution

    |

  15. If 2^(x+y) = 6^(y) and 3^(x-1) = 2^(y+1), then the value of (log 3 - l...

    Text Solution

    |

  16. The value of x satisfying sqrt3^(-4+2log(sqrt5)x)= 1//9 is

    Text Solution

    |

  17. The value of x satisfying the equation root(3)(5)^(log(5)5^(log(5)5^...

    Text Solution

    |

  18. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals

    Text Solution

    |

  19. If log(y) x + log(x) y = 2, x^(2)+y = 12 , then the value of xy is

    Text Solution

    |

  20. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

    Text Solution

    |