Question

Which of the following is true? a. The base of a logarithmic function can be a negative number. b. A logarithmic function is the inverse of a rational function. c. The domain of the logarithmic function f(x) = log5x is all positive real numbers. d. The base of a logarithmic function can be zero.

Answer 1

Option c - The domain of the logarithmic function
`f(x)=\log_5x` is all positive real numbers.

Explanation:

Given : Following statements.

To find : Which of the following is true?

Solution :

a. The base of a logarithmic function can be a negative number.

False, because the base of a logarithmic function is greater than 1.

b. A logarithmic function is the inverse of a rational function.

False, because the inverse of the logarithmic function is an exponential function.

c. The domain of the logarithmic function
`f(x)=\log_5x` is all positive real numbers.

True, because the domain of the logarithmic function
`y=\log_bx` is the set of positive real numbers and the range is the set of real numbers.

d. The base of a logarithmic function can be zero.

False, because the base to zero is when solved by exponent then it became 0 to the power which is always zero.

Therefore, Option c is true.

Answer 2

I think the correct answer among the choices listed above is option C. The only true statement is that the domain of the logarithmic function f(x) = log5x is all positive real numbers. Hope this answers the question. Have a nice day.