CODEWITHSUNDEEP
algorithm
Raman
Raman

Reputation: 2785

Find first digit of 2^n where n is of order 10^5

Today while going through a random video on youtube, I learn't about a very interesting law called Benford's law. I was wondering if it is possible to write a code to verify it for a^n.

I want to write a code that prints the first digit of 2^n where n is of order 10^5. Is it possible to write a code for it?

I know I haven't posted any code sample or shown any research effort.I am unable to think of any algorithm for it.

Upvotes: 1

Views: 396

Answers (1)

r3mainer
r3mainer

Reputation: 24557

Use logarithms.

log_10(2) = 0.30102999566

log_10(2^100000) = 30102.999566

In other words, 2^100000 is a 30103-digit number, whose first digit can be found from the fractional part of this number:

10^0.999566 = 9.9900..

Upvotes: 4

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