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- Logarithmic Functions
Natural log: ln
- Lesson: 13:22
- Lesson: 2a2:18
- Lesson: 2b2:47
Natural log: ln
Basic Concepts: Converting from logarithmic form to exponential form, Evaluating logarithms without a calculator, Common logarithms
Related Concepts: Logarithmic scale: Richter scale (earthquake), Logarithmic scale: pH scale, Logarithmic scale: dB scale
Lessons
• Definition of ‘‘natural logarithm"and mathematical constant ‘‘e":
1)Recall: common logarithms = log with base ‘‘10"example:log3=log103
natural logarithms = log with base ‘‘e" example:ln5=loge5
2)Like ‘‘π", a mathematical constant equal to 3.14….., ‘‘e"is just another mathematical constant equal to 2.71…. .
3)Significance of ‘‘π": we use it in circle calculations:
example: areacircle=πr2 or circumferencecircle=2πr
Significance of ‘‘e": we use it mostly in calculus. ‘‘e"is a unique number such that the slope of tangent line at every point on the graph of f(x)=ex is equal to the y-value of the point.
1)Recall: common logarithms = log with base ‘‘10"example:log3=log103
natural logarithms = log with base ‘‘e" example:ln5=loge5
2)Like ‘‘π", a mathematical constant equal to 3.14….., ‘‘e"is just another mathematical constant equal to 2.71…. .
3)Significance of ‘‘π": we use it in circle calculations:
example: areacircle=πr2 or circumferencecircle=2πr
Significance of ‘‘e": we use it mostly in calculus. ‘‘e"is a unique number such that the slope of tangent line at every point on the graph of f(x)=ex is equal to the y-value of the point.
- 1.Evaluate ln5a)by using the LOG key on a calculator.b)by using the LN key on a calculator.
- 2.Without using a calculator, evaluate:a)lne[useful rule:lne=1]b)eln500[useful rule: elna=a]
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10.
Logarithmic Functions
10.1
What is a logarithm?
10.2
Converting from logarithmic form to exponential form
10.3
Evaluating logarithms without a calculator
10.4
Common logarithms
10.5
Natural log: ln
10.6
Evaluating logarithms using change-of-base formula
10.7
Converting from exponential form to logarithmic form
10.8
Solving exponential equations with logarithms
10.9
Product rule of logarithms
10.10
Quotient rule of logarithms
10.11
Combining product rule and quotient rule in logarithms
10.12
Evaluating logarithms using logarithm rules
10.13
Solving logarithmic equations
10.14
Graphing logarithmic functions
10.15
Finding a logarithmic function given its graph
Don't just watch, practice makes perfect
Practice topics for Logarithmic Functions
10.1
What is a logarithm?
10.2
Converting from logarithmic form to exponential form
10.3
Evaluating logarithms without a calculator
10.4
Common logarithms
10.5
Natural log: ln
10.6
Evaluating logarithms using change-of-base formula
10.7
Converting from exponential form to logarithmic form
10.8
Solving exponential equations with logarithms
10.9
Product rule of logarithms