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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,

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

16.

Logarithmic Functions

16.1

What is a logarithm?

16.2

Converting from logarithmic form to exponential form

16.3

Evaluating logarithms without a calculator

16.4

Common logarithms

16.5

Natural log: ln

16.6

Evaluating logarithms using change-of-base formula

16.7

Converting from exponential form to logarithmic form

16.8

Solving exponential equations with logarithms

16.9

Product rule of logarithms

16.10

Quotient rule of logarithms

16.11

Combining product rule and quotient rule in logarithms

16.12

Evaluating logarithms using logarithm rules

16.13

Solving logarithmic equations

16.14

Graphing logarithmic functions

16.15

Finding a logarithmic function given its graph

We have over 1140 practice questions in AU Year 11 Maths for you to master.

Get Started Now16.1

What is a logarithm?

16.2

Converting from logarithmic form to exponential form

16.3

Evaluating logarithms without a calculator

16.4

Common logarithms

16.5

Natural log: ln

16.6

Evaluating logarithms using change-of-base formula

16.7

Converting from exponential form to logarithmic form

16.8

Solving exponential equations with logarithms

16.9

Product rule of logarithms