Aptitude - Logarithm - Discussion
Discussion Forum : Logarithm - General Questions (Q.No. 11)
11.
If log 2 = 0.30103, the number of digits in 264 is:
Answer: Option
Explanation:
| log (264) | = 64 x log 2 |
| = (64 x 0.30103) | |
| = 19.26592 |
Its characteristic is 19.
Hence, then number of digits in 264 is 20.
Discussion:
59 comments Page 5 of 6.
Omi said:
1 decade ago
If the logarithm to any base a gives characteristic n, then we say that the number of integers possible is given by:
a^(n+1)-a^n.
Here the characteristic is 19 and base is 10, therefore number of possible integers are:
10^(19+1) -10^19.
=>10^20-10^19.
=>10^19 (10-1).
=>9*10^19.
Thus it will have 19 zeroes and last digit 9 i.e.
90000000000000000000! count the digits you will get the answer :).
a^(n+1)-a^n.
Here the characteristic is 19 and base is 10, therefore number of possible integers are:
10^(19+1) -10^19.
=>10^20-10^19.
=>10^19 (10-1).
=>9*10^19.
Thus it will have 19 zeroes and last digit 9 i.e.
90000000000000000000! count the digits you will get the answer :).
Sum said:
1 decade ago
How it will be 20?
Sharad said:
1 decade ago
Why this is not 19 give me the correct reason?
Ashish Agarwal said:
1 decade ago
Why not 19?
Kavitha said:
1 decade ago
What is a need to add 1 i.e. (19+1) ?
B ESWARA RAO(WATSON) said:
1 decade ago
Log(2)^64 = 64log2 = 64(0.30130) = 19.
19+1 = 20. So 2^64 have 20 digits.
19+1 = 20. So 2^64 have 20 digits.
Rohit Singh said:
1 decade ago
The integral part is known as characteristics or exponent and decimal part is known as mantissa.
Sheelu said:
1 decade ago
In this decimal part first decimal is lower than 5, so answer 19 is also right.
Tiwali said:
1 decade ago
@Vicky
You mentioned that, Given the log of a number, we will be able to find out the number of digits that the original number had by knowing the value of the characteristic. Will you explain even more clearly. ?
You mentioned that, Given the log of a number, we will be able to find out the number of digits that the original number had by knowing the value of the characteristic. Will you explain even more clearly. ?
Neha said:
1 decade ago
Can you tell about characterstic and mantissa concept?
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