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88 | eUreka Math algebra II StUdy gUIde
Lesson 8: The “WhatPower” Function
● (^) Students calculate a simple logarithm using the definition.
Lesson 9: Logarithms—How Many Digits Do You Need?
● (^) Students use logarithms to determine how many characters are needed to generate
unique identification numbers in different scenarios.
● (^) Students understand that logarithms are useful when relating the number of digits in
a number to the magnitude of the number and that base-10 logarithms are useful
when measuring quantities that have a wide range of values, such as the magnitude
of earthquakes, volume of sound, and pH levels in chemistry.
Lesson 10: Building Logarithmic Tables
● (^) Students construct a table of logarithms base 10 and observe patterns that indicate
properties of logarithms.
Lesson 11: The Most Important Property of Logarithms
● (^) Students construct a table of logarithms base 10 and observe patterns that indicate
properties of logarithms.
Lesson 12: Properties of Logarithms
● (^) Students justify properties of logarithms using the definition and properties already
developed.
Lesson 13: Changing the Base
● (^) Students understand how to change logarithms from one base to another.
● (^) Students calculate logarithms with any base using a calculator that computes only
logarithms base 10 and base e.
● (^) Students justify properties of logarithms with any base.
Lesson 14: Solving Logarithmic Equations
● (^) Students solve simple logarithmic equations using the definition of logarithm and
logarithmic properties.
Lesson 15: Why Were Logarithms Developed?
● (^) Students use logarithm tables to calculate products and quotients of multi-digit
numbers without technology.
● (^) Students understand that logarithms were developed to speed up arithmetic
calculations by reducing multiplication and division to the simpler operations of
addition and subtraction.
● (^) Students solve logarithmic equations of the form log()XY=log() by equating X and Y.
Topic C: Exponential and Logarithmic Functions and Their Graphs
The lessons covered in Topics A and B build on students’ prior knowledge of the
properties of exponents, exponential expressions, and solving equations by extending
the properties of exponents to all real number exponents and positive real number bases
before introducing logarithms. This topic reintroduces exponential functions, introduces
logarithmic functions, explains their inverse relationship, and explores the features of their
graphs and how they can be used to model data.