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Get Started Now- Lesson: 13:22
- Lesson: 2a2:18
- Lesson: 2b2:47

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,

• 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.

- 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)$\ln e$[useful rule:$\ln e = 1]$b)$e^{\ln500}$[useful rule: $e^{\ln a} = a]$

17.

Exponential and Logarithmic Functions

17.1

Solving logarithmic equations

17.2

Graphing exponential functions

17.3

Graphing transformations of exponential functions

17.4

Finding an exponential function given its graph

17.5

Graphing logarithmic functions

17.6

Finding a logarithmic function given its graph

17.7

Finance: compound interest

17.8

Continuous growth and decay

17.9

Natural log: ln

17.10

Solving exponential equations with logarithms

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