We raise the numbers 2 and 5 to the same positive integer power and get two numbers that have the same first (leftmost) digit. What are the possible values of the first digit?
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$\begingroup$ Well... I believe the only possible number is 3. $\endgroup$ – Samuel Mar 28 '17 at 16:35
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$\begingroup$ First as in leftmost or rightmost? $\endgroup$ – John Mar 28 '17 at 16:37
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$\begingroup$ @John: for the rightmost the only answer is $1$ with the power being $0$. $\endgroup$ – Ross Millikan Mar 28 '17 at 16:42
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$\begingroup$ I don't know how to find the first digit... If it were possible to have the total number n of digits (length of number) and then divide by 10^(n-1) and then round down the quotient... $\endgroup$ – Samuel Mar 28 '17 at 16:44
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$\begingroup$ Just thinking out loud: We can also take the logarithm "L" of the number, take its integer part "i" and then divide by 10^i, then round down the quotient. I don't know if any of these things make sense! $\endgroup$ – Samuel Mar 28 '17 at 16:53
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Hint: what is the product $2^n \cdot 5^n?$
answered Mar 28 '17 at 16:42
