16.3 Natural log: ln
Natural log: ln
Lessons
Notes:
• 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 yvalue of the point.

a)
by using the LOG key on a calculator.

b)
by using the LN key on a calculator.


2.
Without using a calculator, evaluate: