Home
Class 12
MATHS
There exists a natural number N which is...

There exists a natural number `N` which is 50 times its own logarithm to the base 10, then `N` is divisible by 5 (b) 7 (c) 9 (d) 11

A

5

B

7

C

9

D

11

Text Solution

Verified by Experts

The correct Answer is:
A
`N= 50 log_(10) N`
` rArr log_(10) N = N/50`
` rArr N = (10) ^(N//50)`
` rArr N^(1//N) = (10)^(1//50) = (10)^(2//100)= (100)^(1//100`
` :. N = 100`
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

Prove that For any natural number n, 7^n - 2^n is divisible by 5.

n is selected from the set {1, 2, 3,.............,100} and the number 2^n+3^n+5^n is formed. Total number of ways of selecting n so that the formed number is divisible by 4 is equal to (A) 50 (B) 49 (C) 48 (D) None of these.

In the decimal system of numeration of six-digit numbers in which the sum of the digits is divisible by 5 is a. 180000 b. 540000 c. 5xx10^5 d. none of these

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7^m+7^n is divisible by 5, equals (a) 1/4 (b) 1/7 (c) 1/8 (d) 1/49

How many four digit numbers abcd exist such that a is odd, b is divisible by 3, c is even and d prime?

An n-digit number is a positive number with exactly n digit Nine hundred distinct n−digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of n for which this is possible is (a) 6 (b) 7 (c) 8 (d) 9

The number of distinct natural numbers up to a maximum of four digits and divisible by 5, which can be formed with the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9 each digit not occurring more than once in each number, is a. 1246 b. 952 c. 1106 d. none of these

The number of triangles that can be formed with 10 points as vertices n of them being collinear, is 110. Then n is a. 3 b. 4 c. 5 d. 6

CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. If (log)4 5=aa n d(log)5 6=b , then (log)3 2 is equal to 1/(2a+1) (b)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

  7. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. 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

    |

  14. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

    Text Solution

    |

  18. If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...

    Text Solution

    |

  19. If 2x^((log)4 3)+3^((log)4x)=27 , then x is equal to 2 (b) 4 (c) 8 (d...

    Text Solution

    |

  20. The equation log4(2-x)+log(0.25)(2+x)=log4(1-x)+log(0.25)(2x+1) has

    Text Solution

    |