Question

(iv) Check whether (26)" can end with the digit 5 for any n€N

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Answer 1

Yes, it can, for example, 26^(log[26](5)) = 5

But if n is a whole number:

26^0 = 1

26^1 = 26

26^2 = 676

26^3 = 17576

26^4 = 456976

... etc. ...

As you can see, the last digit is always 6 (except 26^0 which is 1). It can never be 5.

And if n is a negative integer, the result contains infinity decimal digits, because 26 is a multiple of 13 which is never divisible into any exponent of 10 (e.g. 10, 100, 1000, etc.). So there is no last digit.