1 thought on “(iv) Check whether (26)” can end with the digit 5 for any n€N<br /><br />”
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.
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.