• Definition of $``$natural logarithm$"$and mathematical constant $``$e$":$

1)Recall: common logarithms = log with base $``10"$example:$\log3 = \log_{10}3$

natural logarithms = log with base $``$e$"$ example:$\ln5 = \log_e5$

2)Like $``\pi"$, a mathematical constant equal to 3.14….., $``$e$"$is just another mathematical constant equal to 2.71…. .

3)Significance of $``\pi"$: we use it in circle calculations:

example: $area_{circle} = \pi r^2$ or $circumference_{circle} = 2 \pi r$

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 $f(x) = e^x$ is equal to the y-value of the point.

1)Recall: common logarithms = log with base $``10"$example:$\log3 = \log_{10}3$

natural logarithms = log with base $``$e$"$ example:$\ln5 = \log_e5$

2)Like $``\pi"$, a mathematical constant equal to 3.14….., $``$e$"$is just another mathematical constant equal to 2.71…. .

3)Significance of $``\pi"$: we use it in circle calculations:

example: $area_{circle} = \pi r^2$ or $circumference_{circle} = 2 \pi r$

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 $f(x) = e^x$ is equal to the y-value of the point.