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 2 of 6.
Sai krishna said:
8 years ago
According to as given in important formulas when there are 2 digits in the left-hand side of decimal value of a logarithm the characteristic is added with 1 less than the no of digits.
so,
no of digs =2 so we should add 1.
hence total = 19+1.
i.e. 20.
so,
no of digs =2 so we should add 1.
hence total = 19+1.
i.e. 20.
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. ?
Srivaisnavi said:
3 years ago
Here 19 is characteristics.
The characteristics represent the (no. of digits of the number - 1 )
So 19= no. of digits -1.
therefore, no. of digits = 19+1 = 20
I hope it's clear.
The characteristics represent the (no. of digits of the number - 1 )
So 19= no. of digits -1.
therefore, no. of digits = 19+1 = 20
I hope it's clear.
(12)
Xiyza said:
5 years ago
The easiest way is.
Since the base is 10.
10^2 = 100 (3 digits).
10^3= 1000 (4 digits).
So on,
Therefore.
10^19 (characteristic part) = 20 digits i.e. (10000000000000000000).
Since the base is 10.
10^2 = 100 (3 digits).
10^3= 1000 (4 digits).
So on,
Therefore.
10^19 (characteristic part) = 20 digits i.e. (10000000000000000000).
(2)
Nitish said:
1 decade ago
Logarithm of a number consists of the two parts.
1. integral part
2. decimal part.
The integral part is called the characteristic and the decimal part is called mantissa.
1. integral part
2. decimal part.
The integral part is called the characteristic and the decimal part is called mantissa.
Prasanna said:
5 years ago
2^64=10^x.
X=log 2^64.
X=19.164.
2^64=10^(19.164)=10^(19+.164)=1.8*10^19=18*10^18.
Hence after 18, There are 18 digits(zeros).
Total digits = 2(i.e. 1,8)+18(zeros) = 20.
X=log 2^64.
X=19.164.
2^64=10^(19.164)=10^(19+.164)=1.8*10^19=18*10^18.
Hence after 18, There are 18 digits(zeros).
Total digits = 2(i.e. 1,8)+18(zeros) = 20.
Anjali Kumari said:
6 years ago
@Pawan here it's given 2^64. You can find the factor of 64 and then calculations will be lengthy. So the given solution is accurate.
Gopi said:
5 years ago
@Vicky.
The value of log 103 is 0.4771 but here are three digits, 1 0 3. How can you say that there is a single digit?
The value of log 103 is 0.4771 but here are three digits, 1 0 3. How can you say that there is a single digit?
Kumar said:
5 years ago
When We Are Finding Number of Digits We Have To Always Add +1 to The Characteristics Value. So, 19 + 1 =20.
Pawan said:
6 years ago
Why we didn't solve like this?
log (2) ^64 as log (2) ^6 then 6*log (2) that is equal to 6*0.3010 = 1.806.
log (2) ^64 as log (2) ^6 then 6*log (2) that is equal to 6*0.3010 = 1.806.
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