Digits

Algebra Level 3

If 2^(2014) has 607 digits, compute the number of digits in 5^(2014).


The answer is 1408.

William Isoroku by William Isoroku , 25, USA

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2 solutions

log 5^(2014)=1407.725

so number of digits = 1408

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Milind Joshi
Jul 22, 2014

(Digits in 2^n)+(Digits in 5^n)=(Digits in 10^n) and we know that digits in 10^n will be (n+1).......so here n=2014.... (Digits in 2^(2014))+(Digits in 5^(2014))=2015......so ans will be 1408

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How do you know that "(Digits in 2^n)+(Digits in 5^n)=(Digits in 10^n)"? In general, such a property doesn't hold ((Digits in a)+(Digits in b) ≠ \neq (Digits in ab). E.g., take a = 10 , b = 10 a=10, b=10 ). Could you elaborate? How to prove this?

mathh mathh - 6 years, 9 months ago

can u please explain in brief how can u get the problem with one more ex-

teja katru - 6 years, 9 months ago

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