Question

Can a logarithm have a base of 1?

Answer 1

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.