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

Oct 25, 2016

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 $x \ne 1$

• 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.