Home
Class 12
MATHS
The value of log ab- log|b|=...

The value of `log ab- log|b|=`

A

log a

B

`log|a|`

C

`-log a`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
log ab is defined if ` ab gt 0` or a and b have the same sign.
Case (i): a, `b gt 0`
` rArr log ab - log|b| = log a + log b - log b = log a` …(i)
Case (ii): ` a, b lt 0`
` rArr log ab - log|b| = log (-a) + log (-b) - log (-b) `
` = log (-a)` ...(ii)
From Eqs. (i) and (ii), we have
` log ab - log|b| = log |a|`.
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

The value of log(ab)^(2) - log(ac) + log(bc^(4)) - 3 log (bc) is:

The value of "log"_(b)a xx "log"_(c) b xx "log"_(a)c , is

The value of (log_(a)(log_(b)a))/(log_(b)(log_(a)b)) is

The value of a^((log_b(log_bx))/(log_b a)), is

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. Given that log(2)=0. 3010 , the number of digits in the number 2000^(...

    Text Solution

    |

  2. If (21. 4)^a=(0. 00214)^b=100 , then the value of 1/a-1/b is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |