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IB DP Maths: AI HL復習筆記1.2.2 Logarithms

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月19日 下午6:01

Introduction to Logarithms

What are logarithms?

Why use logarithms?

  • Logarithms allow us to solve equations where the exponent is the unknown value
    • We can solve some of these by inspection

Exam Tip

  • Before going into the exam, make sure you are completely familiar with your GDC and know how to use its logarithm functions

Worked Exampleai-sl-1-1-2intro-to-logs-we-i

ai-sl-1-1-2intro-to-logs-we-ii

 

 

 

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

6.2.1-Laws-of-Logarithms-Notes-fig2

Useful results from the laws of logarithms

6.2.1-Laws-of-Logarithms-Notes-fig3

  • 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

?aa-sl-1-2-2-laws-of-logs-we-solution-part-a

aa-sl-1-2-2-laws-of-logs-we-solution-part-b

 

 

 

轉載自savemyexams

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