why the base of a logarithmic function must be a positive number?

Answer 1

Because taking a negative number to a non-integer power involves imaginary numbers.

Answer 2

Remember that a negative power means reciprocal.

2^(-3) is NOT -8. It is 1/8

Written log base 2 (1/8) = -3

Also consider looking at the graph of log x on your graphing calculator. See if the domain (the x values) are ever negative. Good luck.

Answer 3

generally base of a logarithm is" 10 "or "e".logarithm is undefined for negative numbers and for zero.we have values for positive numbers of logarithm, and undefined for negatives.