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- Logarithmic Functions

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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: $e^{\ln a} = a]$

32.

Logarithmic Functions

32.1

What is a logarithm?

32.2

Converting from logarithmic form to exponential form

32.3

Evaluating logarithms without a calculator

32.4

Common logarithms

32.5

Natural log: ln

32.6

Evaluating logarithms using change-of-base formula

32.7

Converting from exponential form to logarithmic form

32.8

Solving exponential equations with logarithms

32.9

Product rule of logarithms

32.10

Quotient rule of logarithms

32.11

Combining product rule and quotient rule in logarithms

32.12

Evaluating logarithms using logarithm rules

32.13

Solving logarithmic equations

32.14

Graphing logarithmic functions

32.15

Finding a logarithmic function given its graph

We have over 2080 practice questions in ACT Compass Test Prep for you to master.

Get Started Now32.1

What is a logarithm?

32.2

Converting from logarithmic form to exponential form

32.3

Evaluating logarithms without a calculator

32.4

Common logarithms

32.5

Natural log: ln

32.6

Evaluating logarithms using change-of-base formula

32.7

Converting from exponential form to logarithmic form

32.8

Solving exponential equations with logarithms

32.9

Product rule of logarithms