Integrated Mathematics Change of Base of Logarithms.

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Presentation transcript:

Integrated Mathematics Change of Base of Logarithms

3.6. Change of Base of Logarithms State the rule for the change of base of logarithmic expressions and use it to solve equations involving different bases Syllabus

Find the value of, correct to 4 significant figures: Apply log base 10 on both sides

Re-look into the example: Apply log base 2 on both sides

Re-look into the example: Apply log base 3 on both sides

We can convert to log of any base, c: Apply log base c on both sides

Exercise 3G, Question 1: Evaluate each of the following, giving your answer to 4 significant figures: (b) (c)

Exercise 3G, Question 1: Evaluate each of the following, giving your answer to 4 significant figures: (d) Cannot multiply together because of different base! Change to the same base of 10

Exercise 3G, Question 1: Evaluate each of the following, giving your answer to 4 significant figures: (f) Change to the same base of 10 Not

Exercise 3G, Question 1: Evaluate each of the following, giving your answer to 4 significant figures: (g) Change to the same base of 10

Exercise 3G, Question 1: Evaluate each of the following, giving your answer to 4 significant figures: (h) Change to the same base of 10

Exercise 3G, Question 2: If, express each of the following in terms of p: (iii)(ii) (iv)

Exercise 3G, Question 3: Solve the equation: Change to common base of 3

Exercise 3G, Question 4: Evaluate:

Exercise 3G, Question 5(c): Given that: Evaluate:

Exercise 3G, Question 5(d): Given that: Evaluate: Spot the mistake in the working! ( ) X

Exercise 3G, Question 5(e): Given that: Evaluate:

Exercise 3G, Question 6: Given that: Evaluate:

Exercise 3G, Question 7: Given that:Express in terms of x

Exercise 3G, Question 8: Solve:,

Exercise 3G, Question 8: