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CIE A Level Maths: Pure 3復(fù)習筆記2.2.1 Laws of Logarithms

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月19日 下午3:22

Laws of Logarithms

What are the laws of logarithms?

Laws of Logarithms Notes fig1, A Level & AS Maths: Pure revision notes

  • There are many laws or rules of indices, for example
    • am?x an?= am+n
    • (am)n?= amn
  • There are equivalent laws of logarithms (for a > 0)6.2.1-Laws-of-Logarithms-Notes-fig2
  • There are also some particular results these lead to6.2.1-Laws-of-Logarithms-Notes-fig3?
  • Two of these were seen in the notes Logarithmic Functions
  • Beware …
    • …?log (x + y) ≠ log x + log y
  • Results apply to?ln?too

How do I use the laws of logarithms?

  • Laws of logarithms can be used to …
    • … simplify expressions
    • … solve logarithmic equations
    • … solve exponential equations

    6.2.1-Laws-of-Logarithms-Notes-fig4

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

2-2-1-laws-of-logs-we-solution-1

 

 

 

 

 

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