Write down the largest base?5 positive integer in n digits and the largest base 7 number in m digits. It is necessary to represent n?digit base?5 numbers in base?7. What is the minimum number m of digits needed to represent all possible n?digit base?5 numbers? Hint—the largest m?digit base?7 number should be greater than, or equal to, the largest n?digit base?5 number.
What will be an ideal response?
The largest base?5 number in n digits is 444…4 (n fours) which is 
Similarly, the largest base 7 number in m digits is 
In order to represent all base 5 numbers we have
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