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- Logarithmic Functions

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

8.

Logarithmic Functions

8.1

What is a logarithm?

8.2

Converting from logarithmic form to exponential form

8.3

Evaluating logarithms without a calculator

8.4

Common logarithms

8.5

Natural log: ln

8.6

Evaluating logarithms using change-of-base formula

8.7

Converting from exponential form to logarithmic form

8.8

Solving exponential equations with logarithms

8.9

Product rule of logarithms

8.10

Quotient rule of logarithms

8.11

Combining product rule and quotient rule in logarithms

8.12

Evaluating logarithms using logarithm rules

8.13

Solving logarithmic equations

8.14

Graphing logarithmic functions

8.15

Finding a logarithmic function given its graph

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now8.1

What is a logarithm?

8.2

Converting from logarithmic form to exponential form

8.3

Evaluating logarithms without a calculator

8.4

Common logarithms

8.5

Natural log: ln

8.6

Evaluating logarithms using change-of-base formula

8.7

Converting from exponential form to logarithmic form

8.8

Solving exponential equations with logarithms

8.9

Product rule of logarithms