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Evaluating logarithms using change-of-base formula
- Lesson: 13:21
- Lesson: 2a1:04
- Lesson: 2b1:09
- Lesson: 2c1:21
- Lesson: 2d1:41
- Lesson: 3a3:11
- Lesson: 3b6:47
Evaluating logarithms using change-of-base formula
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
Lessons
• change-of-base rule:logba=logxblogxa=logbloga
• common logarithms:log with base ‘‘10"example: log3=log103
example: logx=log10x
• common logarithms:log with base ‘‘10"example: log3=log103
example: logx=log10x
- 1.How to apply ‘‘change-of-base rule"
Express log53 in three different ways. - 2.Using a calculator, evaluate the following logarithms
by applying ‘‘ change-of-base rule":a)log53b)log7416c)log2257d)6log4999 - 3.Using a calculator, solve for x to the nearest hundredth.a)log6x=log78b)log235=logx0.104
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29.
Logarithms and Exponential Functions
29.1
What is a logarithm?
29.2
Evaluating logarithms without a calculator
29.3
Product rule of logarithms
29.4
Quotient rule of logarithms
29.5
Combining product rule and quotient rule in logarithms
29.6
Solving logarithmic equations
29.7
Evaluating logarithms using change-of-base formula
29.8
Exponential growth and decay by a factor
29.9
Exponential decay: Half-life
29.10
Natural log: ln