Home
Class 12
MATHS
If (21. 4)^a=(0. 00214)^b=100 , then the...

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

A

0

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`(21.4)^(a) = 100`
` rArr a log(21.4) = 2`
` :. Log(21.4) = 2//a` …(i)
From ` (0.00214)^(b) = 100`, we get
` b(log 0.00214)= 2`
` or b log(214.4 xx 10^(-4)) = 2`
` or b = 2/(log 21.4-4) = 2/(2/a-4) = 1/(1/a - 2) = a/(1-2a)`
` rArr 1/b = (1-2a)/a`
` rArr 1/a - 1/b = 2`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|18 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise Exercise 1.6|6 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

Let ab=1 , then the minimum value of (1)/(a^(4))+(1)/(4b^(4)) is

If a + 1/b = b + 1/c = 1, then the value of c + 1/a is

If a^4b^5=1 then the value of log_a(a^5b^4) equals

If P(A | B) = 1/4 , then what is the value of P(A^C/B) ?

Two events A and B are such that P(A)=(1)/(4), P(B//A)=(1)/(2) and P(A//B)=(1)/(4) , then the value of P(A^(c )//B^(c )) is -

Let a ,b >0, let 5a-b ,2a+b ,a+2b be in A.P. and (b+1)^2, a b+1,(a-1)^2 are in G.P., then the value of (a^(-1)+b^(-1)) is _______.

If lim_(xtooo) {(x^(2)+1)/(x+1)-(ax+b)}=0, then find the values of a and b.

Let t_(100)=sum_(r=0)^(100)(1)/(("^(100)C_(r ))^(5)) and S_(100)=sum_(r=0)^(100)(r )/(("^(100)C_(r ))^(5)) , then the value of (100t_(100))/(S_(100)) is (a) 1 (b) 2 (c) 3 (d) 4

If z^3+(3+2i)z+(-1+i a)=0 has one real root, then the value of a lies in the interval (a in R) a.(-2,1) b. (-1,0) c. (0,1) d. (-2,3)

CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)
  1. The number N = 6 log(10) 2+ log(10) 31 lies between two successive in...

    Text Solution

    |

  2. Given that log(2)=0. 3010 , the number of digits in the number 2000^(...

    Text Solution

    |

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

    Text Solution

    |

  4. The value of loga b-log|b|=

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

  7. If p >1 and q >1 are such that log(p+q)=logp+logq , then the value of ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. The value of 3^((log)4 5)-5^((log)4 3) is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |