# 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.

### Student Facing

• I understand how to evaluate a logarithmic expression.

### 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 $$\ln(x)$$.