AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.14 Logarithmic Function Context and Data Modeling
Notes
Log models fit data that grow quickly at first and then level off slowly. Examples: decibels, pH, the Richter scale.
- $f(x)=a+b\ln x$ is a common log regression model.
Practice
pH $=-\log[H^+]$. A solution with $[H^+]=10^{-3}$ has pH:
$-(-3)$.
Data increase quickly, then more and more slowly with no upper limit. A good model:
Logs grow without bound but slowly.
An earthquake of magnitude 6 compared with magnitude 4 is how many times as intense (base-10 scale)?
$10^{6-4}$.
Ready for more? Take the Unit 2 test.