which of the following is true about the base b of a logarithmic function?\no (b > 0) and (b = 1)\no (b > 0)…

which of the following is true about the base b of a logarithmic function?\no (b > 0) and (b = 1)\no (b > 0) and (b\neq1)\no (b < 0) and (b\neq1)\no (b < 0) and (b = 1)

which of the following is true about the base b of a logarithmic function?\no (b > 0) and (b = 1)\no (b > 0) and (b\neq1)\no (b < 0) and (b\neq1)\no (b < 0) and (b = 1)

Answer

Explanation:

Step1: Recall logarithm base conditions

The base (b) of a logarithmic function (y = \log_{b}x) must be positive ((b>0)) because if (b = 1), (\log_{1}x) is not well - defined (since (1^{y}=x) has either no solution for (x\neq1) or infinitely many solutions for (x = 1)), and if (b<0), the function will have non - real values for many (x) values in the real number system. Also, (b\neq1).

Answer:

(b>0) and (b\neq1) (the second option)