Home
Class 12
MATHS
If p >1a n dq >1 are such that log(p+q)=...

If `p >1a n dq >1` are such that `log(p+q)=logp+logq ,` then the value of `log(p-1)+"log"(q-1)` is equal to 0 (b) 1 (c) 2 (d) none of these

A

0

B

1

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`log(p+q) =log p+log q`
` rArr p+q=pq`
` rArr pq-p-q = 0`
` rArr pq-p-q+1 = 1`
` rArr (p-1)(q-1) = 1`
` rArr log(p-1)+log(q-1) = log 1=0`
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 p >1 and q >1 are such that log(p+q)=logp+logq , then the value of log(p-1)+log(q-1) is equal to (a) 0 (b) 1 (c) 2 (d) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

The value of lim_(xto 0)(log(1+2x))/(x) is equal to

(log)_(x-1)x (log)_(x-2)(x-1) (log)_(x-12)(x-11)=2,x is equal to: 9 (b) 16 (c) 25 (d) none of these

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

If (log)_k xdot(log)_5k=(log)_x5,k!=1,k >0, then x is equal to (a) k (b) 1/5 (c) 5 (d) none of these

The value of the integral int_0^oo(xlogx)/((1+x^2)^2)dxi s 0 (b) log 7 (c) 5 log 13 (d) none of these

The value of 0. 2^(logsqrt(5)1/4+1/8+1/(16)+) is 4 b. log4 c. log2 d. none of these

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3-(log)_3 2 log(3/2) (d) none of these

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. If a , b , c are consecutive positive integers and log (log(1+a c)=2K ...

    Text Solution

    |

  2. If (a+(log)4 3)/(a+(log)2 3)=(a+(log)8 3)/(a+(log)4 3)=b ,t h e ni se ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If (log)(10)2=a ,(log)(10)3=bt h e n(log)(0. 72)(9. 6) in terms of aa ...

    Text Solution

    |

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

    Text Solution

    |

  8. The value of ((log)2 24)/((log)(96)2)-((log)2 192)/((log)(12)2) is 3 (...

    Text Solution

    |

  9. (log)(x-1)x (log)(x-2)(x-1) (log)(x-12)(x-11)=2,x is equal to: 9 (b) ...

    Text Solution

    |

  10. If f(x)=log((1+x)/(1-x)),t h e n f(x1)f(x)=f(x1+x2) f(x+2)-2f(x+1)...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  13. If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y)...

    Text Solution

    |

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

    Text Solution

    |

  15. The value of x satisfying the equation 3sqrt(5)^(log)5 5^(((log)5(log)...

    Text Solution

    |

  16. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals odd integer (b)...

    Text Solution

    |

  17. if (log)y x+(log)x y=1,x^2+y=12 , the value of x y is 9 (b) 12 (c) 15 ...

    Text Solution

    |

  18. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

    Text Solution

    |

  19. If (x+1)^((log)(10)(x+1))=100(x+1), then

    Text Solution

    |

  20. If log2x+logx2=10/3=log2y+logy2 and x!=y ,then x+y=

    Text Solution

    |