# 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 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 non-integer values.

Provide students with access to scientific calculators during the last activity and the cool-down.

### 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

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 $$\ln(x)$$.