Going deeper: properties of logarithms (optional)
• Understand and explain the properties of logarithms.
• Use properties of logarithms to solve problems.
The sections previous to this one are sufficient to meet the standards about logarithms in CCSSM including the (+) standards. Students pursuing STEM careers will need to go further. This section and the next one show the bridging material needed for STEM readiness.
The properties of logarithms arise naturally from the properties of exponents and the fact that logarithmic functions are inverse to exponential functions. In this section students are given opportunities to notice patterns when combining logarithmic expressions with operations (for example, $\log(A)+\log(B)$ is equal to $\log(AB)$), conjecture that these patterns could be useful shortcuts, and then justify why the patterns always work.
WHAT: In this lesson, students make and use slide rules to discover the properties of logarithms (MP5, MP7).
WHY: The technique, analogous to number-line addition, gives opportunities for students look for a make use of structure (MP.7) In this case, the use of powers and logarithms as mappings between additive and multiplicative structures on the number line.