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

10.

Logarithmic Functions

10.1

What is a logarithm?

10.2

Converting from logarithmic form to exponential form

10.3

Evaluating logarithms without a calculator

10.4

Common logarithms

10.5

Natural log: ln

10.6

Evaluating logarithms using change-of-base formula

10.7

Converting from exponential form to logarithmic form

10.8

Solving exponential equations with logarithms

10.9

Product rule of logarithms

10.10

Quotient rule of logarithms

10.11

Combining product rule and quotient rule in logarithms

10.12

Evaluating logarithms using logarithm rules

10.13

Solving logarithmic equations

10.14

Graphing logarithmic functions

10.15

Finding a logarithmic function given its graph

We have over 1380 practice questions in NZ Year 11 Maths for you to master.

Get Started Now10.1

What is a logarithm?

10.2

Converting from logarithmic form to exponential form

10.3

Evaluating logarithms without a calculator

10.4

Common logarithms

10.5

Natural log: ln

10.6

Evaluating logarithms using change-of-base formula

10.7

Converting from exponential form to logarithmic form

10.8

Solving exponential equations with logarithms

10.9

Product rule of logarithms