Question

Which of the following is true?

The base of a logarithmic function can be zero.

A logarithmic function is the inverse of a rational function.

The domain of the function f(x) = log5x is all real numbers less than zero.

The range of the function f(x) = log5x includes rational numbers.

Answer 1

The last one is true. The domain of the log function are all real numbers less than zero and negatives. If it's 5x inside the log, of 4x, or something like \[\frac{x^2-1}{x}\] it's just a question of not letting this inside the log be zero or negative. As the statement says only about the zero, it is incorrect. The last one is ok because log(5x) has some rational numbers in its range. These include log(5*2) = 1 for example.

Answer 2

The range of the function f(x) = log5x includes rational numbers. so this is true?

Answer 3

Yes, only this one is true. as log(10) is 1 and 1 is a rational number. It includes also other ones like log(5*20)=log(100) = 2.

Answer 4

thanks!