IB DP Maths: AA HL复习笔记1.2.2 Laws of Logarithms
What are the laws of logarithms?
- Laws of logarithms allow you to simplify and manipulate expressions involving logarithms
- The laws of logarithms are equivalent to the laws of indices
These laws are in the formula booklet so you do not need to remember them
- You must make sure you know how to use them
Useful results from the laws of logarithms
- These useful results are not in the formula booklet but can be deduced from the laws that are
Laws of logarithms can be used to …
- simplify expressions
- solve logarithmic equations
- solve exponential equations
Exam Tip
- Remember to check whether your solutions are valid
- log (x+k) is only defined if x > -k
- You will lose marks if you forget to reject invalid solutions
Worked Example
Change of Base
Why change the base of a logarithm?
- The laws of logarithms can only be used if the logs have the same base
- If a problem involves logarithms with different bases, you can change the base of the logarithm and then apply the laws of logarithms
- Changing the base of a logarithm can be particularly useful if you need to evaluate a log problem without a calculator
- Choose the base such that you would know how to solve the problem from the equivalent exponent
How do I change the base of a logarithm?
- The formula for changing the base of a logarithm is
This is in the formula booklet- The value you choose for b does not matter, however if you do not have a calculator, you can choose b such that the problem will be possible to solve
Exam Tip
- Changing the base is a key skill which can help you with many different types of questions, make sure you are confident with it
- It is a particularly useful skill for examinations where a GDC is not permitted
Worked Example
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