Home
Class 11
MATHS
Let x=(0. 15)^(20)dot Find the character...

Let `x=(0. 15)^(20)dot` Find the characteristic and mantissa of the logarithm of `x` to the base 10. Assume `(log)_(10)2=0. 301a n d(log)_(10)3=0. 477.`

Text Solution

Verified by Experts

`x=(0.15)^20`
taking log both side
`logx=log(0.15)^20`
`logx=10log(0.15)`
`20log(15/100)=20[log15-2]`
`20[log5+log3-2]`
`20[log(10/2)+log3-2]`
`20[log10-log2+log3-2]`
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

  • PERMUTATIONS AND COMBINATIONS

    CENGAGE ENGLISH|Exercise All Questions|444 Videos

Similar Questions

Explore conceptually related problems

Let x=(0. 15)^(20)dot Find the characteristic and mantissa of the logarithm of x to the base 10. Assume log_(10)2=0. 301 and log_(10)3=0. 477.

If mantissa of lagarithm of 719.3 to the base 10 is 0.8569 then mantissa of logarithm of 71.93 is

Find the approximate value of (log)_(10)1005 , given that (log)_(10)e=0. 4343

Find the approximate value of (log)_(10)1005 , given that (log)_(10)e=0. 4343

[log_10⁡(x)]^2 − log_10⁡(x^3) + 2=0

Using differentials, find the approximate value of (log)_(10)10. 1 , it being given that (log)_(10)e=0. 4343 .

Comprehension 3 If P is the non negative characteristic of (log)_(10)N , the number of significant digit in N\ i s\ P+1 . If P is the negative characteristic of (log)_(10)N , then number of zeros after decimal before a significant digit start are P-1.( Use log_(10)\ 2=0. 301.(log)_(10)3=0. 4771 ) Number of significant digit in N , where N=(5/3)^(100), is- a. 23 b. \ 22 c. \ 21 d. none

Comprehension 3 If P is the non negative characteristic of (log)_(10)N , the number of significant digit in N\ i s\ P+1 . If P is the negative characteristic of (log)_(10)N , then number of zeros after decimal before a significant digit start are P-1.( Use log_(10)\ 2=0. 301.(log)_(10)3=0. 4771 ) Number of zeros after decimal before a significant digit start in N , where N=((81)/(16))^(-25)i s- a. 16 b. \ 17 c.18 d. 19

Solve (x^(log_(10)3))^(2) - (3^(log_(10)x)) - 2 = 0 .

Let S denotes the antilog of 0.5 to the base 256 and K denotes the number of digits in 6^(10) (given log_(10)2=0.301 , log_(10)3=0.477 ) and G denotes the number of positive integers, which have the characteristic 2, when the base of logarithm is 3. The value of SKG is

CENGAGE ENGLISH-LOGARITHM-All Questions
  1. If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)(4a)3a ,p rov et h a t1+x y z=...

    Text Solution

    |

  2. Let L denote antilog32 0.6 and M denote the number of positive integer...

    Text Solution

    |

  3. Let x=(0. 15)^(20)dot Find the characteristic and mantissa of the loga...

    Text Solution

    |

  4. Using logarithms, find the value of 6.45 x 981.4

    Text Solution

    |

  5. In the 2001 census, the population of India was found to be 8. 7x10^7d...

    Text Solution

    |

  6. If (log)(10)2=0. 30103 ,(log)(10)3=0. 47712 , then find the number of...

    Text Solution

    |

  7. If a=(log)(12)18 , b=(log)(24)54 , then find the value of a b+5(a-b)do...

    Text Solution

    |

  8. Solve the equations for x and y:(3x)^(log3)=(4y)^(log 4), 4 ^(log x) ...

    Text Solution

    |

  9. If (log)k xdot(log)5k=(log)x5,k!=1,k >0, then x is equal to k (b) 1/5...

    Text Solution

    |

  10. If p , q in N satisfy the equation x^sqrt(x)=(sqrt(x))^x, then p a n ...

    Text Solution

    |

  11. Solution set of the inequality (log)(0. 8)((log)6(x^2+x)/(x+4))<0 is

    Text Solution

    |

  12. Which of the following is not the solution of (log)3(x^2-2)<(log)3(3/2...

    Text Solution

    |

  13. The true solution set of inequality (log)((x+1))(x^2-4)>1 is equal to ...

    Text Solution

    |

  14. Solve the following equation of x :2(log)x a+(log)(a x)a+3(log)(a^2x)a...

    Text Solution

    |

  15. The x , y , z are positive real numbers such that (log)(2x)z=3,(log)(5...

    Text Solution

    |

  16. Which of the following, when simplified, reduces to unity? (a) (log)(...

    Text Solution

    |

  17. If (log)a x=b for permissible values of a and x , then identify the ...

    Text Solution

    |

  18. The number of positive integers satisfying x+(log)(10)(2^x+1)=x(log)(1...

    Text Solution

    |

  19. Solve: (1/2)^(log^(10a^2))+2>3/(2^((log)(10)(-a)))

    Text Solution

    |

  20. Write the characteristic of each of the following numbers by using ...

    Text Solution

    |