Aptitude - Logarithm - Discussion

There is actually no relationship between CHARACTERISTICS and DIGITS OF NUMBER.

Here log(2^64) = 64*log 2 = 64*0.3010 = 19.265.

Then, the equation of NUMBER OF DIGITS = NUMBER WHICH IS ON LEFT SIDE OF DECIMAL POINT + 1.

Therefore, here in this case -> 19+1=20.

Characteristics is one less than the number of digits on the left of the decimal.

Hence, the answer we got 19 is characteristic since we used log. And it has 2 digits and char would be 1.

Now, the actual number of digits is 20. Why? because no. Of digits is one more than characteristics. Here the question actually doesn't have log so then we take the no. 19 and add char +1.

@Gopi.

Value of log (103) is 2.01 so number Of digits are 2+1.

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).

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.

Nice explanation. Thanks all.

Thanks for explaining @Vicky.

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).

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.