A function f is said to be one-to-one if each range value corresponds to exactly one domain value.
If f is a one-to-one function, then the inverse of f is the function formed by interchanging the independent and dependent variables for f. Thus, if (a, b) is a point on the graph of f, then (b, a) is a point on the graph of the inverse of f.
Note: If f is not one-to-one, then f does not have an inverse.
The inverse of an exponential function is called a logarithmic function. For b > 0 and b ≠ 1,
y = logb x is equivalent tox = by.
The log to the base b of x is the exponent to which b must be raised to obtain x.
Drag the slider to see the graph of the exponential and logarithmic functions for different values of b.
b = 2
If b, M, and N are positive real numbers with b ≠ 1, and p and x are real numbers, then:
|logb 1 = 0||logb b = 1|
|logb bx = x||blogbx = x, x > 0|
|logb MN = logb M + logb N||logb M/N = logb M - logb N|
|logb Mp = p logb M||logb M = logb N if and only if M = N|