Logarithms

Topic outline

• Outomes

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  In this course you will learn:
  

  1. What logarithms (logs) are.
  2. How to apply the log laws.
  3. How to simplify logs.
  4. To solve log equations.

  
  

• What are logs?

  Logarithms or logs for short, are another way to express exponents. There are 3 types of logs; common, binary and natural. In this course we will cover common logs where the base of the log is 10.

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    From exponential to log form

    Logs and exponents are inverses. Logs were invented as an easier way to do long calculations at a time when calculators did not exist. 

    
    

    For an introduction to logs and to learn how to convert from exponential to log form watch the next video. After you have watched the video try the activity that follows to see if you can change from exponential to log form and back again.

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    Convert between logs and exponents H5P

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• The log laws

  Just as exponents have rules to make them easier to simplify so too do logarithms. The log laws are very similar to exponent laws.

   

  Make sure you understand how to use the log laws to simply expressions by watching the next video (it has 2 parts and you need to view both). You may also read a summary and work through examples of log laws by clicking on Logarithmic Properties and Functions.

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    Practise using the log laws

    You can practise the properties of logs by trying the exercises: Use the properties of logarithms AND Evaluate logarithms. Also try the activity that follows.

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    More practise on log properties H5P

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• Simplify logs

  Some questions may require you to work with more than one log property at a time. The next example uses multiple steps to simplify logs. Test your understanding of using multiple log properties by trying the quiz that follows.

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    Use log laws to simplify Quiz

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• Solve log equations

  When logs were first invented they were the most efficient way to work with very large numbers. But, these days there are many calculators and programs (log calculator) that can solve log equations for us very quickly. 

  In this section, we will go over solving logs by hand as they were traditionally done using the laws of exponents and logs.

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    Solving log equations by hand

    Watch the next video to learn how solve simple log equations manually. 

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    Practise solving log equations

    When you have mastered basic log equations click the link to the exercise to solve more complex log equations, make sure to attempt the question first before looking at the solution: Solving logarithmic equations

• For enrichment

  Historically log tables were used to perform long calculations that scientific calculators now do with ease. If you would like to read about how log tables were used you can visit: How to use Logarithmic tables. 

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    Attribution & licence Page

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