Because logarithms can only be taken of positive numbers, and
a logarithm equation just might be converted to an equation that
has a 0 or negative solution.

 log(13 – 5x) = log(1 – x)

We use the principle that we convert log(A) = log(B) to A = B

    13 - 5x = 1 - x
        -4x = -12
          x = 3

But when you check it you find that this is an extraneous solution:

 log(13 – 5(3)) = log(1 – 3)
   log(13 - 15) = log(-2)
        log(-2) = log(-2)

This may look like it checks except for the fact that logs of negative
numbers do not exist in real numbers.  So there is no solution in
real numbers.

Edwin