# Graphing logarithmic and exponential functions

### Graph of logarithmic functions

- Graphing logarithmic functions follows the same rules as graphing other functions. For example if we were to graph \(y=\log(x)\) we would need to remember that logarithms are not defined for negative values of \(x\) or for \(x=0\). That is the domain is \(x>0\).
- Firstly, draw up a table of values:

\(x\) | \(0.01\) | \(0.1\) | \(1\) | \(10\) | \(100\) |

\( y = \log_{10}(x) \) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) |

- Secondly, plot the points:

- Simple Logarithmic graphs all have similar shapes to the figure above.
- The domain is restricted and includes only real numbers greater than zero (you cannot find a logarithm of a negative number).
- There will be an \(x\)-intercept, in this case \(x=1\).
- As the independent variable decreases (approaches zero) the dependent variable approaches negative infinity.
- As the independent variable increases (approaches infinity, \(\infty\)) the dependent variable increases slowly.