Question

Using the definition of a logarithmic function where `y=log_bx`, why can't the base b equal 1?

Answer 1

See explanation.

Explanation:

According to definition of logarithmic function it must be defined for all positive real numbers and if we tried to construct such assignment for `b=1` then it would have

• NO values for `x != 1`

• infinitely many values for `x=1`

because for all real numbers `x` different from zero `1^x=1`

therfore it would not be a function.