# Problem of the day !

We have started one more interesting feature of the blog
I will be posting problem of the day , and the best answer will be highly appreciated

If you win problem of the day for more than 4 times in a  week then I will send you a mathematics very interesting E-Book

So here is Question 1 )

QUESTION 1 )

How many digits does the number 21000 contain?

NOTE :

I am a young student who loves math . I like number theory and inequalities part the most , and preparing for Math Olympiads :)

Posted on Monday,May 28, 2012, in Problems and tagged , , . Bookmark the permalink. 8 Comments.

1. Aayush Kumar

5 digits are there
2,1,0,0,0
and 3 different digits are there
2,1 and 0
we can have in expanded form total we can see that there are numbers till ten thousand so we can count that the numbers are 5 in number so we have the required answer 5,.

2. Akash Agarwal

Let
x = 2^1000,
Taking log wrt base 10,
log x = 1000log2
log x = 301.03
Thus x should be of 302 digits so that log x lies between 301 and 302.
Thus 2^1000 has 302 digits.

3. Aayush Kumar

Hey! Its not seeming that there is any power with my mobile

• keshushivang

aayush kumar : it is 2^1000

4. keshushivang

Let
x = 2^1000,
Taking log wrt base 10,
log x = 1000log2
log x = 301.03
Thus x should be of 302 digits so that log x lies between 301 and 302.
Thus 2^1000 has 302 digits.

Is absolutely correct 🙂 🙂

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7. Nishant

the number of digits is logn+1
n=2^1000 taking log on both sides
logn=1000log2(base 10 here)
logn=1000*.3010
log n = 301.03…
the number of digits is 301+1=302…