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IB DP Maths: AA HL复习笔记1.2.2 Laws of Logarithms
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月11日 下午12:17
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
U
seful 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 G
DC
is not permitted
Worked Example
转载自savemyexams
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