Exponential and logarithm function
In an exponential function, the variable x is as a power
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.
Definition of logarithm
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.
The 10-base logarithm is usually denoted by lg (log in some calculators). Therefore
has the domain
Graphs of logarithmic functions
logkx is the inverse of the function kx