0
$\begingroup$

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?

$\endgroup$
10
  • $\begingroup$ Well... I believe the only possible number is 3. $\endgroup$ – Samuel Mar 28 '17 at 16:35
  • $\begingroup$ First as in leftmost or rightmost? $\endgroup$ – John Mar 28 '17 at 16:37
  • $\begingroup$ @John: for the rightmost the only answer is $1$ with the power being $0$. $\endgroup$ – Ross Millikan Mar 28 '17 at 16:42
  • $\begingroup$ 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
  • $\begingroup$ 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
0
$\begingroup$

Hint: what is the product $2^n \cdot 5^n?$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.