Help me please! How many digits are in the number 2^2009 × 5^2005? I've no idea how to begin.

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Originally Posted by judocallin02 Help me please! How many digits are in the number 2^2009 × 5^2005? I've no idea how to begin. Take logs to base 10: . My calculator gives that as 2006.2041, which means that lies between and . Alternatively, , from which you can estimate the answer. The second method is much cleaner in this case, but the log-to-base-ten method works more generally.

thanks

Hello, judocallin02! I recommend Opalg's second method . . . How many digits are in the number: . ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Therefore, the product has digits.

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