Question

Which of the following statements is true?
a) An exponential function is never the inverse of a logarithmic function.
b)The base of the logarithmic function f(x) = log5x is 5.
c) The range of the logarithmic function f(x) = log5x is all real numbers less than zero.
d) The domain of the logarithmic function f(x) = log5x is all real numbers.

Note: the 5 after log is really small

Answer 1

BY DEFINITION, the logarithm is the inverse of the corresponding exponential function, so you know that's false. The correspondence is in the following manner.\[a^b=c \ \Leftrightarrow\ \log_a c = b\]Here, \(a\) is called the base in both cases, since it is the base of the exponential. Check the domain and range of the logarithm function either by reflecting the corresponding exponential function about the line \(y=x\) as you would do for any inverse, or graph it (all logarithms have the same general shape).