Exponential and logarithm function

Exponential function

In an exponential function, the variable x is as a power

Example 1

Graph of f(x)

Graph of g(x)

The domain of the exponential function are all real numbers. All exponential functions pass through the point (0,1). If the base a > 1 function is strictly increasing. If 0 < a <1 the function is strictly decreasing. Note that the exponential function only gets positive values.

Logarithmic function

Definition of logarithm

Example 2

When we want to solve an equation

It can be concluded that x = 3. Mathematically, this is denoted by

It states: “The 2-base logarithm of the number 8” is therefore the number to which 2 must be raised to obtain 8.

Example 3

The 10-base logarithm is usually denoted by lg (log in some calculators). Therefore

Logarithmic function

has the domain

Example 4

Graphs of logarithmic functions


logkx is the inverse of the function kx