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

1 Answer
Daniel L.
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 != 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.

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