Common and Natural Logarithms and Solving Equations
Change of base formula.
Students continue an examination of logarithms in the Research and Revise stage by studying two types of logarithms—common logarithms and natural logarithm. In this study, they take notes about the two special types of logarithms, why they are useful, and how to convert to these forms by using the change of base formula. Then students can solidify their understanding with the associated activity to see how these types of logarithms can be applied to solve exponential equations. They compute a set of practice problems and apply the skills learned in class.
All types of engineers use natural and common logarithms.Chemical engineers use them to measure radioactive decay, and pH solutions, which are measured on a logarithmic scale. Exponential equations and logarithms are used to measure earthquakes and to predict how fast your bank account might grow. Biomedical engineers use them to measure cell decay and growth, and also to measure light intensity for bone mineral density measurements, the focus of this unit.
After this lesson, students should be able to:
- Define the number e.
- Define the common and natural logarithms.
- Use common and natural logarithms to evaluate expressions.
- Use the change of base formula to convert to a common or natural logarithm in order to evaluate expressions and solve equations.