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:
10^{3} = 1,000 is the same as: 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 = log_{2}(A)
 2 = log_{2}(B)
 3 = log_{2}(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. 