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Sine and Cosine Law
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Logarithmic Laws
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Logarithmic Laws
Below are a list of Logarithmic Laws which are considered assumed knowledge for the course.
1) \( \log(a) + \log(b) = \log(ab) \)
2) \( \log(a) - \log(b) = \log(\frac{a}{b}) \)
3) \( \log(a^r) = r\log(a) \)
4) \( \log_e (x) = \ln(x) \)
5) \( \log_a (a) = 1 \) such that \( \log_a (a^x) =x \)
6) \( \log_a x = \frac {\ln(x)}{\ln(a)} \)
7) \( a^{\log_a x} = x \)
For logarithms involving a base of ln:
1) \( \ln(a) + \ln(b) = \ln(ab)\)
2) \( \ln(a) - \ln(b) = \ln(\frac{a}{b}) \)
3) \( \ln(a^r) = r\ln(a) \)
4) \( \ln (e) = 1 \) such that \( \ln (e^x) =x \)
5) \(e^{\ln x} = x \)
Note that these are the same as the standard logarithmic equations.
Deriving Logarithmic Functions:
1) \( \frac{d}{dx} ( \ln (x) ) = \frac {1}{x} \)
2) \( \frac{d}{dx} ( \ln (u) )= \frac {u'}{u} \) ie. \( \frac{d}{dx} ( \ln (x^2)) = \frac {2x}{x^2} \)
Home
Tips for new Engineers
Free Useful Programs and Information Sources
University Website Tips and Tricks
Surviving University
Learning Resources
First Year Engineering
>
Engineering Sustainability and Professional Practice
>
What is this course about?
Concepts
>
Cultural Awareness
Wicked Problems
EWB Challenge
Foundation of Engineering Design
>
What is this course about?
Energy in Engineering Systems
>
What is this course about?
Engineering Computation
>
What is this course about?
Statics
>
Sine and Cosine Law
Mathematics: Single variable Calculus and differential equations
>
What is this course about?
Logarithmic Laws
Week One:
Workshop One:
Identity Sheet
Introductory Engineering Mathematics
>
Week1
Engineering Computation
>
week 3
Other
>
The Business of IT
>
Helpful links
Notes
Practice Final Exam
Information Security
Databases
Networks