Home
Class 11
MATHS
If a,b,c are any three consecutive integ...

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

A

`"log" b`

B

`"log" ((b)/(2))`

C

`"log" (2b)`

D

`2"log"b`

Text Solution

Verified by Experts

The correct Answer is:
D
Since a, b, c are three consective positive integers,
`therefore b = a + 1, c= a + 2 " and " 2b = a+ c`
Now,
`"log" (1+ca)`
`= "log"{1+(a+2)a} = "log" (a+1)^(2) = 2"log" (a+1) = 2 "log" b`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|66 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • INEQUALITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise EXERCISE SECTION-II (Assertion-Reason )|1 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Write down three consecutive integers preceding -531 .

If a, b and c are consecutive integers, what is a+b+c ?

Write three consecutive odd integers preceding -69 .

If a,b and c are three consecutive positive integers such that 1/(a!)+1/(b!)=lambda/(c!) then find the value of root under lambda .

Write down three consecutive integers succeeding -29 .

If a, b, c are three consecutive terms of an A.P. and x,y,z are three consecutive terms of a G.P., then prove that x^(b-c) . y^(c-a).z^(a-b)=1

If 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an A.P., prove that a ,b ,c are the three consecutive terms of a G.P.

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

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

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

OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Section I - Solved Mcqs
  1. If loga=1/2 logb=1/5logc then a^4b^3c^(-2)=

    Text Solution

    |

  2. If a=log(24)12,b=log(48)36 and c=log(36)24, abc is equal to

    Text Solution

    |

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

    Text Solution

    |

  4. If ("log"(a)x)/("log"(ab)x) = 4 + k + "log"(a)b, "then" k=

    Text Solution

    |

  5. If a = 1 + log(x) yz, b = 1 + log(y) zx and c = 1 + log xy where x, ...

    Text Solution

    |

  6. (1)/("log"(2)n) + (1)/("log"(3)n) + (1)/("log"(4)n) + … + (1)/("log"(4...

    Text Solution

    |

  7. If n is a natural number such that n=P1^(a1)P2^(a2)P3^(a3)...Pk^(ak) ...

    Text Solution

    |

  8. Prove that number (log)2 7 is an irrational number.

    Text Solution

    |

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

    Text Solution

    |

  10. If (1)/("log"(2)a) + (1)/("log"(4)a) + (1)/("log"(8)a) + (1)/("log"(16...

    Text Solution

    |

  11. If "log"(3) a xx "log"(a) x = 4, then x is equal to

    Text Solution

    |

  12. The value of x^("log"(x) a xx "log"(a)y xx "log"(y) z) is

    Text Solution

    |

  13. If "log"(ax)x, "log"(bx) x, "log"(cx)x are in H.P., where a, b, c, x b...

    Text Solution

    |

  14. If the left hand side of the equation a(b-c)x^2+b(c-a) xy+c(a-b)y^2=...

    Text Solution

    |

  15. If loga/(b-c) = logb/(c-a) = logc/(a-b), then a^(b+c).b^(c+a).c^(a+b)...

    Text Solution

    |

  16. Solve log(2)|4-5x| gt 2.

    Text Solution

    |

  17. The sum of the series "log"(4)2-"log"(8)2 + "log"(16)2- "log"(32) 2...

    Text Solution

    |

  18. If log0.3(x-1)ltlog0.09(x-1), then x lies in the interval

    Text Solution

    |

  19. The values of x satisfying x^("log"(5)) gt5 lie in the interval

    Text Solution

    |

  20. The solution set of the equation "log"(x)2 xx "log"(2x)2 = "log"(4x...

    Text Solution

    |