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

12.

Logarithmic Functions

12.1

What is a logarithm?

12.2

Converting from logarithmic form to exponential form

12.3

Evaluating logarithms without a calculator

12.4

Common logarithms

12.5

Natural log: ln

12.6

Evaluating logarithms using change-of-base formula

12.7

Converting from exponential form to logarithmic form

12.8

Solving exponential equations with logarithms

12.9

Product rule of logarithms

12.10

Quotient rule of logarithms

12.11

Combining product rule and quotient rule in logarithms

12.12

Evaluating logarithms using logarithm rules

12.13

Solving logarithmic equations

12.14

Graphing logarithmic functions

12.15

Finding a logarithmic function given its graph

We have over 1040 practice questions in AU Year 12 Maths for you to master.

Get Started Now12.1

What is a logarithm?

12.2

Converting from logarithmic form to exponential form

12.3

Evaluating logarithms without a calculator

12.4

Common logarithms

12.5

Natural log: ln

12.6

Evaluating logarithms using change-of-base formula

12.7

Converting from exponential form to logarithmic form

12.8

Solving exponential equations with logarithms

12.9

Product rule of logarithms