Home
Class 11
MATHS
(log)4 18 is a rational number (b) an...

`(log)_4 18` is a rational number (b) an irrational number a prime number (d) none of these

Text Solution

Verified by Experts

`=log_4 18`
`=log_4(9*2)=log_4 9+log_4 2`
`=log_(2^2)^(3^2)+log_(2^2)^2`
`=(2/2)log_2^3+1/2log_2^2`
`=log_2^3+1/2`
`=1+1/2=3/2`
This is rational.
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE|Exercise Solved Examples And Exercises|67 Videos

  • PERMUTATIONS AND COMBINATIONS

    CENGAGE|Exercise Solved Examples And Exercises|433 Videos

Similar Questions

Explore conceptually related problems

tan 5^@ is (A) rational number (B) Irrational number (C) prime number (D) none of these

If x be a rational number and y be an irrational number, then :

The product of a rational number and an irrational number is

Is pi a rational or an irrational numbers?

Write a rational number and an irrational number between 1 and 2.

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

All the rational numbers are irrational also.

CENGAGE-LOGARITHM-Solved Examples And Exercises
  1. Given that log(2)=0. 3010 , the number of digits in the number 2000^(...

    Text Solution

    |

  2. The number of N=6-(6(log)(10)2+(log)(10)31) lies between two successi...

    Text Solution

    |

  3. (log)4 18 is a rational number (b) an irrational number a prime num...

    Text Solution

    |

  4. Solve: (log)((2x+3))(6x^2+23x+21)+(log)((3x+7))(4x^2+12 x+9)=4

    Text Solution

    |

  5. Given aa n db are positive numbers satisfying 4(log(10)a)^2+((log)2b)...

    Text Solution

    |

  6. If ((log)a N)/((log)c N)=((log)a N-(log)b N)/((log)b N-(log)c N),w h e...

    Text Solution

    |

  7. If (log)b a(log)c a+(log)a b(log)c b+(log)a c(log)bc=3 (where a , b ,...

    Text Solution

    |

  8. Solve for: x :(2x)^((log)b2)=(3x)^((log)b3) .

    Text Solution

    |

  9. Let a=(log)3(log)3 2. An integer k satisfying 1<2^(-k+3^((-a)))<2, mus...

    Text Solution

    |

  10. The value of 6+(log)(3/2)[1/(3sqrt(2)) * sqrt{ (4 - 1/(3sqrt(2))) sqr...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If (a+(log)4 3)/(a+(log)2 3)=(a+(log)8 3)/(a+(log)4 3)=b ,then b is eq...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. There exists a natural number N which is 50 times its own logarithm t...

    Text Solution

    |

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

    Text Solution

    |