Natural log: ln
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Topic Notes
• 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.
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