Lesson 11
Evaluating Logarithmic Expressions
Lesson Narrative
The purpose of this lesson is to continue building students’ facility in working with logarithmic expressions and equations. Students practice interpreting logarithmic expressions and evaluating them mentally by playing a game of “war.” They also begin to use a calculator to evaluate logarithms. They notice that most values produced by a calculator are also approximations rather than exact values.
In playing the game and evaluating log expressions repeatedly, students look for regularity in how log values could be compared (MP8). They may notice how the size of the parameters in a log expression relates to its value and use their observations (for example, that certain numbers produce positive or negative log values) to make comparisons more efficiently and accurately (MP7).
Learning Goals
Teacher Facing
 Calculate the value of a logarithmic expression using estimation or technology.
 Justify (orally) why one logarithmic expression is greater than another.
Student Facing
 Let’s find some logs!
Required Materials
Required Preparation
When printing and cutting up cards from the blackline master, decide whether to use only the first 20 cards, which contain only logarithms with integer values, or to also include the last 10 cards marked “challenge,” which contain logarithms with noninteger values.
Provide students with access to scientific calculators during the last activity and the cooldown.
Learning Targets
Student Facing
 I can use known values of logarithms to estimate the value of other logarithms.
 I can use technology to determine the value of a logarithm.
CCSS Standards
Addressing
Glossary Entries

logarithm
The logarithm to base 10 of a number \(x\), written \(\log_{10}(x)\), is the exponent you raise 10 to get \(x\), so it is the number \(y\) that makes the equation \(10^y = x\) true. Logarithms to other bases are defined the same way with 10 replaced by the base, e.g. \(\log_2(x)\) is the number \(y\) that makes the equation \(2^y = x\) true. The logarithm to the base \(e\) is called the natural logarithm, and is written \(\ln(x)\).