Aptitude - Logarithm - Discussion

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.

As given in important formulas when there are 'n' digits in the left-hand side of the decimal value of a logarithm the characteristic is added with 1 less than the no of digits.

So,
no. of digs =2(i.e.19) so we should add 1.
hence total = 19+1.
i.e. 20.

If there were 3 digits e.g. 345.8909: its characteristic will be "345" and number of digits =347 (i.e. 345+2).

Why 2? because no. of digs in characteristic = 3 and (3-1=2).

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).

Nice explanation. Thanks all.

For example 2^3=8 has 1 digit, but log 2^3 = 3*log2 = 3 (.301) = 0.903 so avoiding decimal part we get 0.

So, from given data, derived answer should be added with +1 to get original answer so finding digits use this.

Formula x^n= (log x^n) + 1 digits.

Let me solve another problem to understand easier:

10^2 = (log 10^2) + 1 = 2*log10 +1 =2 (1) +1 = 3 digits.

Now let us find digits in 2^64.

Log 2^64= (64*log 2) + 1 as->[ x^n = (log x^n) + 1 ].
=64* (0. 301) +1.
=20. 2.
Here don't confuse about the decimal part so let us take only 20.

Hence answer=20.

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.

How 19+1 came? Explain.

@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.

@Eswara Rao.

Why adding 1 with 19?