• 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.