Introduction to Logarithms
What are logarithms?
- A logarithm is the inverse of an exponent
- If then , where
- This is the essential definition of a logarithm
- The number is called the base of the logarithm
- If then , where
- Try to get used to ‘reading’ logarithm statements to yourself
- means “ is the power that you raise to, to get "
- So means “3 is the power that you raise 5 to, to get 125”
- Two important special cases are:
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- Where is the mathematical constant 2.718…
- This is called the natural logarithm and will have its own button on your calculator
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- Logarithms of base 10 are frequently used
- They are often abbreviated simply as
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Why use logarithms?
- Logarithms allow us to solve equations where the exponent is the unknown value
- We can solve some of these by inspection
- For example, for the equation we know that must be
- But logarithms allow us to solve more complicated problems
- For example, the equation does not have an obvious answer
- Instead we can rewrite the equation as a logarithm
- We can solve some of these by inspection
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- and use our calculator to find the decimal value of
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Exam Tip
- Make sure you are completely familiar with your calculator's logarithm functions
Worked example
Solve the following equations:
Use the definition of a logarithm to rewrite this as an exponential equation
This can be solved by inspection
Use the definition of a logarithm to rewrite this as a logarithm equation
Use your calculator to find the value of that logarithm
Round to 3 significant figures