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 : 

You have to give solution of your answer too 

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About shivang1729

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. 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. 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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  4. 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.

    Is absolutely correct 🙂 🙂

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  7. 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…

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