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- Logarithmic Functions

Still Confused?

Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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

40.

Logarithmic Functions

40.1

What is a logarithm?

40.2

Converting from logarithmic form to exponential form

40.3

Evaluating logarithms without a calculator

40.4

Common logarithms

40.5

Natural log: ln

40.6

Evaluating logarithms using change-of-base formula

40.7

Converting from exponential form to logarithmic form

40.8

Solving exponential equations with logarithms

40.9

Product rule of logarithms

40.10

Quotient rule of logarithms

40.11

Combining product rule and quotient rule in logarithms

40.12

Evaluating logarithms using logarithm rules

40.13

Solving logarithmic equations

40.14

Graphing logarithmic functions

40.15

Finding a logarithmic function given its graph

We have over 2420 practice questions in ACCUPLACER Test Prep for you to master.

Get Started Now40.1

What is a logarithm?

40.2

Converting from logarithmic form to exponential form

40.3

Evaluating logarithms without a calculator

40.4

Common logarithms

40.5

Natural log: ln

40.6

Evaluating logarithms using change-of-base formula

40.7

Converting from exponential form to logarithmic form

40.8

Solving exponential equations with logarithms

40.9

Product rule of logarithms