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# 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.