Provide an appropriate response.Why can't 1 be the base of a logarithmic function?

Question

What will be an ideal response?

Answer 1

Answers may vary. One possibility: If the base of a logarithm were 1, as in y = log₁, then for all values of y, x would equal 1. A function requires each x-coordinate to have a unique y-coordinate. Thus, the equation y = log₁, whose graph would be equivalent to the line  would not be a function.