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# UCD Maths Support Centre

Graph of a Log Function

This interactive GeoGebra worksheet allows you to see what the graph of y=loga(x) looks like for values of a from 0.1 to 10 by moving the slider. Have a go and see what happens!

You should note the following.

If a>1, then:

• As x increases so does y.
• y is only defined for positive values of x.
• As x gets close to zero, y gets very large and negative.
• loga(x) is negative if x is less than one and positive if x is greater than one.
• loga(1)=0.
• As a decreases, the graph gets steeper.

If 0<a<1, then:

• As x increases y decreases.
• y is only defined for positive values of x.
• As x gets close to zero, y gets very large and positive.
• loga(x) is positive if x is less than one and negative if x is greater than one.
• loga(1)=0.
• As a increases, the graph gets steeper.

If a=1 then the graph does not exist.

If you want to see approximately what the graph of the natural logarithm looks like then let a=2.7 (remember that e=2.718...).

If you want to return the slider to its original position, then simply click on the icon in the top right hand corner of the worksheet.