2.11 ExpLog - Logarithmic Finding Rule

University:
High School
Course:
High School Physics
Academic year:

2024
Views:

56

Pages:

7
Author:

1 1

2.11 FINDING THE RULE OF LOGARITHMS SIMPLIFIED STANDARD FORM Find rule with fewer parameters 𝒇 𝒙 = log 𝒄 ±(𝒙 − 𝒉) + 𝒌 where: 𝒃 = 𝟏 if 𝒅𝒐𝒎 𝒇 = ]𝒉, ∞[ 𝒃 = −𝟏 if 𝒅𝒐𝒎 𝒇 = ] − ∞, 𝒉[ GIVEN ASYMPTOTE AND 2 POINTS 1. Are points to left 𝒃 = −𝟏 or right 𝒃 = 𝟏 of asymptote? 2. Sub in asymptote for 𝒉 𝒙 = 𝒉 3. Create 2 rules using points 4. Solve the system 1. Right 𝒃 = 𝟏 EX 1 1. Are points to left 𝒃 = −𝟏 or right 𝒃 = 𝟏 of asymptote? 𝑓 𝑥 = log 𝑐 𝑥 − ℎ + 𝑘 2. 𝒉=𝟐 3. 0 = log 𝑐 (3 − 2) + 𝑘 4. − log 𝑐 1 = 𝑘 2. Sub in asymptote for 𝒉 𝒙=𝒉 3. Create 2 rules using points 4. Solve the system 𝑓 𝑥 = log 3 𝑥 − 2 − log 3 1 = 𝑘 𝑘=0 1 = log 𝑐 5 − 2 + 𝑘 1 = log 𝑐 3 − log 𝑐 1 1 = log 𝑐 3 𝑐1 = 3 𝑐=3 EX 2 1. Are points to left 𝒃 = −𝟏 or right 𝒃 = 𝟏 of asymptote? 2. Sub in asymptote for 𝒉 𝒙=𝒉 3. Create 2 rules using points 1. L𝐞𝐟𝐭 𝒃 = −𝟏 𝑓 𝑥 = log 𝑐 − 𝑥 − ℎ 2. +𝑘 𝒉 = −𝟔 3. 4. 4. Solve the system 𝑓 𝑥 = log 1 − 𝑥 + 6 3 +4 GIVEN A TABLE subt div 6/49 7 7 7 6/7 6 42 x f(x) -97/49 3 -13/7 4 -1 5 5 6 47 7 5 = log 7 (−1 − ℎ) + 𝑘 6 = log 7 (5 − ℎ) + 𝑘 𝑘 = 5 − log 7(−1 − ℎ) 6 = log 7(5 − ℎ) + 5 − log 7 (−1 − ℎ) 𝑘 = 5 − log 7 (1) 1 = log 7 (5 − ℎ) − log 7 (−1 − ℎ) 𝑘=5 5−ℎ 1 = log 7 ( ) −1 − ℎ 5−ℎ 1 −7 − 7ℎ = 5 − ℎ 7 = −1 − ℎ ℎ = −2 HOMEWORK Visions 1 P186: 12ace