Logarithms: A Discovery Approach Using Technology

Purpose: Students will discover the basic concept of logarithms.

Materials: A set of scientific calculators.

Background: This lab was done in an urban seventh grade pre-algebra class.

Log Base 10:

  1. Show students how to use the log button - enter number ,then press "log."
  2. Have students find the log of the following
    • 10,
    • 100
    • 1,000
    • 10,000
    • 100,000

  3. Have students conjecture what is meant by "log." (*1)
  4. Have test their conjectures by finding the log of 1 and 1,000,000
  5. Have students predict the value for log(5), log(50), and log(500).
  6. Discuss: Do These answers make sense? (*2)

Comments:

*1: When we covered this, most students could quickly see the logarithm meant the number of zeros. One student recognized that "log" meant a power of 10 and explained it to the class. Since we had not done scientific notation yet, none noticed the relationship between logarithms and scientific notation.

*2: Some students will say that log(50) does not make sense, because there is no way to multiply 10s to get 50. However, they should be able to see that: log(10) < log(50) < log(100).

Extension 1 - Base 2:

Once students understand that log is the inverse of exponents [eg: 103 = 1,000 <---> log(1,000) = 3], have them predict values for log base 2. Use log base 10 to predict the value of the variables.

  • 1 = log(10)
  • 2 = log(100)
  • 3 = log(1,000)
  • 1 = log2(A)
  • 2 = log2(B)
  • 3 = log2(C)

Extension 3: Comparing logarithms to Scientific Notation

Have students compare the how logarithms represent large and small numbers to how scientific notation represents extreme numbers: what similarities and differences do they notice?

See how the Safety Index Chart connects them.

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