Lesson 5 Common Sense Solidify Understanding
Learning Focus
Use logarithms to solve exponential equations.
Solve systems of equations that contain exponential functions.
How can we use logarithms and algebraic reasoning to help us solve exponential equations?
Open Up the Math: Launch, Explore, Discuss
You already know that our number system is base
See how the base is just assumed to be
Each of the sections below contains puzzles for you to solve about base
Table Puzzles
1.
Find the missing values of
a.
b.
c.
When you were trying to find
Table a:
Table b:
2.
What strategy did you use to find the solutions to these equations when you were filling in the tables?
Graph Puzzles
3.
The graph of
a.
Label the solution with an
b.
Label the solution with a
c.
Label the solution with a
4.
Let’s look a little closer at the solutions that you obtained from the graph. Consider the equation:
Would you get the same result if you took the base
Keep going now by rewriting both sides, using logarithm properties.
5.
Let’s try it again with
6.
Why does this process give the same value as the graph?
7.
One of the equations you wrote in the table puzzles was:
How could you unwind this equation using basic operations and logarithms? Show your steps here.
Now you’re ready for the equation puzzles. Here we go!
Equation Puzzles
Solve each equation for
8.
9.
10.
11.
12.
13.
Combo Puzzles
Choose any method to solve.
14.
15.
16.
Ready for More?
Solve the equation
Method 1: Use a base
Method 2: Use a base
Takeaways
Strategies for solving exponential equations and systems:
Vocabulary
- common logarithm
- Bold terms are new in this lesson.
Lesson Summary
In this lesson, we found solutions to base
1.
The graphs of
a.
Make a list of the features of the function
b.
Make a list of the features of
2.
Use long division to calculate
Write your answer as a quotient and a remainder.