Aptitude - Logarithm - Discussion

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.

When We Are Finding Number of Digits We Have To Always Add +1 to The Characteristics Value. So, 19 + 1 =20.

The logarithm of a number contains two parts, namely 'characteristic' and 'mantissa'.

Characteristic: The internal part of the logarithm of a number is called its characteristic.

Case I: When the number is greater than 1.

In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.

Case II: When the number is less than 1.

In this case, the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and it is negative.

Instead of -1, -2 etc. we write 1 (one bar), 2 (two bar), etc.

Why +1 ?

@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.

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.

Good, Thanks @Vicky.

Simply we can calculate the number of digits in the given mathematical operation as below;

Here, the number of digits in 2^64 to be find then we have to calculate value of log 2^64.

So, log 2^64 = 19.26592.

And the result segregated as

19 is characteristic and 0.26592 is mantissa.

finally, we got 19 as characteristic so simply we can say the number of digits in 2^64 is 19+1=20.

Hence 20 is the correct answer.

@Sheelu.

If it is greater than 5 then?

@All.

A logarithm consists of two parts:-.

1. The integral part called the characteristic and.
2. The decimal part called the mantissa.

It's a rule that to find a number of digits of any log, we just have to add 1 to the characteristic of the log.

For example, 2^64.

Log 2^64= 64*log 2.
=64* (0.301).
=19.2.

In this case, 19 is the characteristic.
So a number of digits is= 19+1.
=20.

Hence answer=20.