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Mathematics 21 Online
OpenStudy (anonymous):

How many digits does the number 2^1000 contain?

OpenStudy (anonymous):

I guess 301

OpenStudy (anonymous):

301

OpenStudy (anonymous):

302 :D

OpenStudy (anonymous):

well that's lame -.-

OpenStudy (anonymous):

sorry :)

OpenStudy (anonymous):

lol that's alright

OpenStudy (anonymous):

do they have an explanation?

OpenStudy (anonymous):

mostly

OpenStudy (anonymous):

As 21000 is not a multiple of 10, it follows that, 10m 21000 10m + 1, where 10m contains m + 1 digits. Solving 21000 = 10k, where m k m + 1 k = log 21000 = 1000 log 2 301.02999... , so m = [1000 log 2] = 301. Hence 21000 contains 302 digits. What

OpenStudy (anonymous):

some things did not copy paste nicely :)

OpenStudy (anonymous):

alright I'm done for today, thanks for the problems :)

OpenStudy (anonymous):

It was enough for me too

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