Properties of Logarithms - Maple Help
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Properties of Logarithms

Properties of Logarithmic Functions

Let , , let  and  be positive numbers, and let  be any real number. Then the following properties hold:

 

1. 

The range of  is all real numbers.

2. 

The domain of  is all positive real numbers.

3. 

For ,  for  and  for ; for  the inequalities reverse.

4. 

5. 

6. 

7. 

8. 

9. 

If  and  then . If  and  then . That is,  is an increasing function if  and a decreasing function if .

10. 

 exactly when . That is, the logarithmic and exponential functions with the same base are inverses of each other. In particular, .

Using the properties of logarithms

The calculator shown here is missing a few keys (no multiplication or division keys). Nonetheless, it is still possible to perform any arithmetic calculation involving only +, -, ×, or ÷ operations. This is because the calculator has "10 to the power of" and "logarithm base 10" keys.

 

Try it out. Can you compute these values?

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4/3

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• 

The "log" button represents the base 10 logarithmic function. The calculator displays answers to 2 decimal places.

 

    

   

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