# 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 2^{1000} contain?

NOTE :

You have to give solution of your answer too

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Posted on Monday,May 28, 2012, in Problems and tagged counting, number theory, problem of the day. Bookmark the permalink. 8 Comments.

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,.

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.

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aayush kumar : it is 2^1000

Is absolutely correct 🙂 🙂

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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…