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Year 12/AS Pure Chapter 14.8 (Exponentials and Logarithms)
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This video shows how we can use logarithms to transform graphs of two variables that have an exponential curve into models that have a linear relationship between the same two variables. This makes the relationship between the two variables easier to interpret and understand.
#exponentials #logarithms #9MA0
Introduction: 00:00
Solution to Warm-Up Q1: 0:55
Solution to Warm-Up Q2: 3:28
Solution to Warm-Up Q3: 4:56
Solution to Warm-Up Q4: 8:18
LOGARITHMS AND NON-LINEAR DATA - Introduction: 11:26
Task 1 - Sketching the graph of 𝒚 = 0.2 x 3ˣ : 11:44
Task 2 - Graphing logy (= log( 0.2 x 3ˣ)): 14:20
Task 2a): 14:30
Task 2b): 17:45
Task 2c): 19:02
Explanation of why graphing log( 0.2 x 3ˣ) against 𝒙 produces a straight line: 22:37
Comparing log equation to equation of line of best fit from Task 2: 26:00
CASE 1: Transforming 𝒚 = abˣ to a straight line using logs: 27:43
CASE 2: Transforming 𝒚 = a𝒙ⁿ to a straight line using logs: 30:44
Worked Example 1a): 36:15
Worked Example 1b): 38:27
Worked Example 1c): 39:08
Worked Example 1d): 40:02
Worked Example 1e): 43:41
Worked Example 2a): 48:14
Worked Example 2b): 49:23
Worked Example 2c): 52:19
Suggested Exercises: 54:08
#exponentials #logarithms #9MA0
Introduction: 00:00
Solution to Warm-Up Q1: 0:55
Solution to Warm-Up Q2: 3:28
Solution to Warm-Up Q3: 4:56
Solution to Warm-Up Q4: 8:18
LOGARITHMS AND NON-LINEAR DATA - Introduction: 11:26
Task 1 - Sketching the graph of 𝒚 = 0.2 x 3ˣ : 11:44
Task 2 - Graphing logy (= log( 0.2 x 3ˣ)): 14:20
Task 2a): 14:30
Task 2b): 17:45
Task 2c): 19:02
Explanation of why graphing log( 0.2 x 3ˣ) against 𝒙 produces a straight line: 22:37
Comparing log equation to equation of line of best fit from Task 2: 26:00
CASE 1: Transforming 𝒚 = abˣ to a straight line using logs: 27:43
CASE 2: Transforming 𝒚 = a𝒙ⁿ to a straight line using logs: 30:44
Worked Example 1a): 36:15
Worked Example 1b): 38:27
Worked Example 1c): 39:08
Worked Example 1d): 40:02
Worked Example 1e): 43:41
Worked Example 2a): 48:14
Worked Example 2b): 49:23
Worked Example 2c): 52:19
Suggested Exercises: 54:08
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