Lesson 10
Interpreting and Writing Logarithmic Equations
Lesson Narrative
In this lesson, students continue to develop their understanding of logarithms by working with expressions and equations in some bases other than 10. They analyze a base 2 logarithm table and use it to evaluate logarithmic expressions and solve equations.
Students also learn that an equation written in exponential form has an equivalent equation in logarithmic form. They practice writing equivalent equations in both forms, reinforcing the connection between the structures of a logarithm and an exponential expression (MP7). Use of technology to evaluate logarithms is not recommended in this lesson.
Learning Goals
Teacher Facing
 Coordinate (orally and in writing) exponential and logarithmic equations that represent the same relationship.
 Create equivalent equations in exponential and logarithmic forms.
Student Facing
 Let’s look at logarithms with different bases.
Learning Targets
Student Facing
 I understand how to evaluate a logarithmic expression.
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 \(\ln(x)\).