Can a logarithm have a base of 1?

1 Answer
KillerBunny
Oct 26, 2015

It would make no sense

Explanation:

Think about the meaning of the logarithm in a certain base #a#: you have that #log_a(x)=y# if #a^y=x#. But if #a=1#, then #a^y=1# for any #y#. So, you would have chosen a base which can only give #1# as the result of any power, and so the function would be defined only in one point: the only possible question is "what exponent I must give to #1# to obtain #1#?" Because for any other number #x#, the question "what exponent I must give to #1# to obtain #x#?" would be impossible.

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