To encourage students’ comprehension of the dose response principle, an introduction to what the “natural log” (ln) is and how it behaves is recommended. This will help students to create and analyze a dose response graph.
Students will be able to:
- Define a log as the inverse of an exponentials.
- Explain the benefit of a natural log for biologists.
- Calculate the natural log of a number.
- Plot a logarithmic graph.
National Science Education Standards
Math Strand 2 - Data Analysis, Probability, & Discrete Mathematics
Concept 1: Data Analysis (Statistics)
PO 1. Formulate questions to collect data in contextual situations.
PO 2. Organize collected data into an appropriate graphical representation.
PO 3. Display data as lists, tables, matrices, and plots
Strand 5: Structure & Logic
Concept 1: Algorithms and Algorithmic Thinking
Logs are the inverse of exponentials. This relationship can be expressed as:
bx = y is equivalent to logb(y) = x
- Pronounced "log-base-b of y equals x"
- "b" is called "the base of the logarithm”
- The base b for a logarithm is always positive and not equal to 1
- The value inside the logarithm is called the "argument" of the log
A logarithm can be defined with any base, but the most common base is 10 (log on a standard calculator is log base 10)
- Logarithms with a base e are called the natural logarithm (ln on a calculator)
- The natural log is commonly used in biology and engineering because of the "natural" properties of the exponential function which enable it to describe growth or decay
- e is an irrational number, whose decimal value is approximately 2.71828182845904.
Related and Resource Websites
http://www.purplemath.com/modules/logs3.htm http://www.purplemath.com/modules/graphlog.htm http://www.themathpage.com/alg/logarithms.htmhttp://en.wikipedia.org/wiki/Natural_logarithm