**Exponential and logarithm function**

**Exponential function**

**Exponential function**

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

**Example 1**

**Graph of ****f(x)**

**Graph of**

**f(x)****Graph of ****g(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**

**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

Note!

log_{k}x is the inverse of the function k^{x}