Question

Which of the following is true?

A logarithmic function is the inverse of an exponential function.

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

The domain of the logarithmic function f(x) = log2x is all real numbers.

The range of the logarithmic function f(x) = log2x is all real numbers less than zero

Answer 1

first

Answer 2

Why?

Answer 3

It is defined that way. You can define the exponential function first and then the logarithmic function will be defined as its inverse. Alternatively, you can define the logarithmic function first and the exponential function will then be defined as its inverse. Or I suppose you could define them both and then prove the inverse relationship, but I've never seen it done that way.

Answer 4

So the first one is true?

Answer 5

The way I prefer is to define log x as the integral from 1 to x of 1/t dt, then defining exp as its inverse. Yes, the first one is true.

Answer 6

Thank YOU:)