IB DP Maths: AA SL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

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