 # MA004: Intermediate Algebra

Unit 5: Functions   This unit will introduce you to functions in general, operations on functions, and inverse functions. This is a very important unit especially for students that will be continuing to calculus. You will also learn about two very important functions: the exponential function and its inverse, the logarithmic function. You will also study various applications of these functions. The exponential function has many applications. One of the most common applications is to calculate compound interest.

Unit 5 Time Advisory
Completing this unit should take approximately 27.5 hours.

Subunit 5.1: 4 hours

☐    Subunit 5.2: 4.5 hours

☐    Subunit 5.3: 4.5 hours

☐    Subunit 5.4: 3 hours

☐    Subunit 5.5: 3 hours

☐    Subunit 5.6: 4 hours

☐    Subunit 5.7: 4.5 hours

Unit5 Learning Outcomes
Upon successful completion of this unit, you will be able to:  - determine the domain of a function; - evaluate functions at numerical and variable inputs; - evaluate a sum, product, difference, and quotient of functions at numerical and variable inputs; - compute the composition of two functions; - determine the inverse of a function; - graph quadratic functions by identifying key points; - find compound and continuous interest; and - solve exponential and logarithmic equations.

5.1 Functions   - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.1: Function Notation” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.1: Function Notation” (PDF)

Instructions: Read Section 10.1 in Chapter 10 of your textbook, pages 386–392, to learn about functions and functional notation. Functions are relations between two variables (in general denoted by x and y, where x is the independent variable and y is the dependent variable) such that for each value of x there is only one value of y. Note that this reading covers the topics in Subunits 5.1.1–5.1.4.

Reading this section and taking notes should take approximately 2 hours.

• Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Functions” Link: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook“Functions” (PDF)

Instructions: Complete pages 96–99 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.1.1–5.1.4, and then review the worksheet as you follow along with the videos for solutions.

Completing this assessment should take approximately 1 hour.

5.1.1 Definition and Vertical Line Test of Functions   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Definition and Vertical Line Test” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Definition and Vertical Line Test” (YouTube)

Instructions: Watch the video linked above, which discusses the definition of a function as well as the vertical line test. Functions are relations between two variables (in general denoted by x and y, where x is the independent variable and y is the dependent variable) such that for each value of x there is only one value of y. If a relationship between x and y is graphed, one can determine if the relationship is a function by using the vertical line test. The graph represents a function if every vertical line intersects the graph at most once.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.1.2 Domain of a Function   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Domain” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Domain” (YouTube)

Instructions: Watch the video linked above, which explains the notion of the domain of a function. The domain of this function contains all values that can replace x such that you can calculate y. Speaking geometrically, this means all values of x such that a vertical line through x will intersect the graph.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.1.3 Function Notation   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Function Notation” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Function Notation” (YouTube)

Instructions: Watch the video linked above, which discusses function notation. The explicit function notation is f(x), so you write y = f(x), which means y is a function of x. This is a convenient notation to explicitly define a function and evaluate. For instance, to write y = f(3) means “what is y when x = 3?”

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.1.4 Function Evaluation at Expression   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.1.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Evaluate at Expression” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Functions – Evaluate at Expression” (YouTube)

Instructions: Watch the video linked above, which discusses evaluating a function at an algebraic expression. In the last video, you saw how to evaluate at a number, say f(3) for instance. Using the same concept, you can evaluate at an algebraic expression, for instance f(x+3).

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.2 Algebra of Functions   - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.2: Operations on Functions” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.2: Operations on Functions” (PDF)

Instructions: Read Section 10.2 in Chapter 10 of your textbook, pages 393–400, to learn the algebra of functions. As in arithmetic, you can add, subtract, multiply, and divide functions. There is an additional but important operation called composites. A composite of a function with another function is a function at the second function. You write (f°g)(x) = f(g(x)). Note that this reading covers the topics in Subunits 5.2.1–5.2.3.

Reading this section and taking notes should take approximately 2 hours.

• Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Algebra of Functions” Link: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Algebra of Functions” (PDF)

Instructions: Complete pages 100–101 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.2.1–5.2.3, and then review the worksheet as you follow along with the videos for solutions.

Reading this section and taking notes should take approximately 1 hour.

5.2.1 Add/Subtract/Multiply/Divide Functions (Part 1)   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.2.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of Functions – Add/Subtract/Multiply/Divide (Part 1)” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of Functions – Add/Subtract/Multiply/Divide (Part 1)” (YouTube)

Instructions: Watch the video linked above, which discusses the arithmetic of functions. In a very natural way, you can add, subtract, multiply, and divide functions. This video gives examples of each.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.2.2 Add/Subtract/Multiply/Divide Functions (Part 2)   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.2.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of Functions – Add/Subtract/Multiply/Divide (Part 2)” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of Functions – Add/Subtract/Multiply/Divide (Part 2)” (YouTube)

Instructions: Watch the video linked above, which provides another example of the basic arithmetic of functions.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.2.3 Composition of Functions   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.2.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of Functions – Composition” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Algebra of Functions – Composition” (YouTube)

Instructions: Watch the video linked above, which discusses composition of functions. You can compose functions and use the circle to indicate this. You write (f°g)(x) = f(g(x)).

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.3 Inverse Functions   - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.3: Inverse Functions” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.3: Inverse Functions” (PDF)

Instructions: Read Section 10.3 in Chapter 10 of your textbook, pages 401–405, to learn about inverse functions. Knowing the inverse function of a function can be very helpful in solving many equations in the same way it is helpful to understand that subtraction is the inverse of addition and squaring is the inverse of square root. Note that this reading also covers the topics in Subunits 5.3.1–5.3.3.

Reading this section and taking notes should take approximately 2 hours.

• Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Inverse Functions” Link: Tyler Wallace’s Intermediate Algebra Lab Notebook“Inverse Functions” (PDF)

Instructions: Complete pages 102–104 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.2.1–5.3.3, and then review the worksheet as you follow along with the videos for solutions.

Completing this assessment should take approximately 1 hour.

5.3.1 Determine If Functions Are Inverses   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.3.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse Functions – Showing Functions Are Inverses” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse Functions – Showing Functions Are Inverses” (YouTube)

Instructions: Watch the video linked above, which discusses how to determine if a function is the inverse of another function. The inverse function undoes what a function does to a value of x. For instance, if f(x) = x + 3, then g(x) = x - 3 is the inverse. The test to determine the inverse is (f°g)(x) = (g°f)(x) = x.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.3.2 Find the Inverse of a Function   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.3.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse Functions – Find the Inverse” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse Functions – Find the Inverse” (YouTube)

Instructions: Watch the video linked above, which discusses how to find the inverse of a function. If y = f(x) is the function, then the inverse function, denoted by f-1(x), can be found by solving for x and then replacing y with x and x with y.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.3.3 Graph the Inverse of a Function   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.3.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse Functions – Graph the Inverse” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Inverse Functions – Graph the Inverse” (YouTube)

Instructions: Watch the video linked above, which illustrates how to graph the inverse of a function. The inverse of a function is interchanging the role of the x and y. Graphically, this means that the graph of an inverse function is a reflection across the line y = x.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.4 Graph Quadratic Functions   - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 9, Section 9.11: Graphs of Quadratics” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 9, Section 9.11: Graphs of Quadratics” (PDF)

Instructions: Read Section 9.11 in Chapter 9 of your textbook, pages 380–384, to learn the characteristics of the graphs of quadratics. When graphed, the quadratic function has several characteristics. Each quadratic function graph has a vertex (a point where the graph stops going down and starts going up or vice versa), a line of symmetry, and a maximum value or a minimum value. Note that this reading covers the topics in Subunits 5.4.1 and 5.4.2.

Reading this section and taking notes should take approximately 2 hours.

• Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Graph Quadratic Functions” Link: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook“Graph Quadratic Functions” (PDF)

Instructions: Complete page 105 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.4.1 and 5.4.2, and then review the worksheet as you follow along with the videos for solutions.

Completing this assessment should take approximately 30 minutes.

5.4.1 Graph Key Points of Quadratic Functions (Part 1)   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.4.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Graph Quadratic Functions – Key Points (Part 1)” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Graph Quadratic Functions – Key Points (Part 1)” (YouTube)

Instructions: Watch the video linked above, which discusses the key points of the graph of the quadratic function. This video describes what direction the graph is (either U shaped or up-side-down U shaped), the y-intercept, the x-intercept, and the vertex of the graph.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.4.2 Graph Key Points of Quadratic Functions (Part 2)   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.4.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Graph Quadratic Functions – Key Points (Part 2)” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Graph Quadratic Functions – Key Points (Part 2)” (YouTube)

Instructions: Watch the video linked above, which gives an additional example of finding key points on the graph of the quadratic function.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.5 Exponential Functions   - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.4: Exponential Functions” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.4: Exponential Functions” (PDF)

Instructions: Read Section 10.4 in Chapter 10 of your textbook, pages 406–409, to learn about exponential functions. The exponential function is very important for many applications, but the most common application is for certificate of deposits calculations. Note that this reading also covers the topics in Subunits 5.5.1–5.5.2.

Reading this section and taking notes should take approximately 2 hours.

Termsof Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to Tyler Wallace and the original version can be found here.

• Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Exponential Equations and Exponential Functions” Link: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook“Exponential Equations and Exponential Functions” (PDF)

Instructions: Complete pages 106–107 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.5.1 and 5.5.2, and then review the worksheet as you follow along with the videos for solutions.

Completing this assessment should take approximately 30 minutes.

5.5.1 Exponential Equations with a Common Base   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.5.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Exponential Equations – Common Base” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Exponential Equations – Common Base” (YouTube)

Instructions: Watch the video linked above, which discusses exponential equations with a common base. When an equation consisting of two exponential expressions has the same base and the unknown value is in the exponent, then the exponents must be equal.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.5.2 Exponential Equations with Binomial Exponents   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.5.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Exponential Equations – Binomial Exponents” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Exponential Equations – Binomial Exponents” (YouTube)

Instructions: Watch the video linked above, which gives another example of an equation with a common base and equating the exponents.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.6 Compound Interest   - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.6: Application: Compound Interest” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.6: Application: Compound Interest” (PDF)

Instructions: Read Section 10.6 in Chapter 10 of your textbook, pages 414–419, to learn an application of the exponential functions, namely compound interest. A bank has certificates of deposits (CDs) for sale. The interest rate paid is determined by the length of time that the consumer chooses. The bank will compound the interest (calculate the interest, and then pay interest on this interest) during various intervals of time (quarterly, monthly, annually). Once all of these parameters are known, the compound formula calculates the return on your CD. Note that this reading also covers the topics in Subunits 5.6.1–5.6.4.

Reading this section and taking notes should take approximately 2 hours.

• Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Compound Interest” Link: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook“Compound Interest” (PDF)

Instructions: Complete pages 108–111 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.6.1–5.6.4, and then review the worksheet as you follow along with the videos for solutions.

Completing this assessment should take approximately 1 hour.

5.6.1 Compound Interest with N Compounds per Year   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – N Compounds” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – N Compounds” (YouTube)

Instructions: Watch the video linked above, which discusses an application of the exponential function, namely compound interest. The video gives the formula for return of money (future value of your money) and gives an example.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.6.2 Finding the Principle (P) Given the Return Amount (A)   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Find Principle” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Find Principle” (YouTube)

Instructions: Watch the video linked above, which reverses the equation discussed above. These examples ask, knowing how much money you want returned, how much do you need to invest?

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.6.3 Continuous Compounding   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Continuous Compounds” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Continuous Compounds” (YouTube)

Instructions: Watch the video linked above, which discusses an application of the exponential function, namely continuous compounding interest. Continuous compounding means the bank is compounding every millisecond of every day. When this happens, a new constant is introduced: e. e is a constant and is approximately equal to 2.7182818. Then the formula becomes A = Pert.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.6.4 Finding the Principle (P) for Continuous Compounding   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.6.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Finding Principle with Continuous Interest” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Compound Interest – Finding Principle with Continuous Interest” (YouTube)

Instructions: Watch the video linked above, which asks the reverse of the examples above for continuous compound interest. This video illustrates how to calculate the amount needed to invest when given how much one earns.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 15 minutes.

5.7 Logarithms (Logs)   - Reading: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.5: Logarithmic Functions” Link: Washington State Board for Community and Technical Colleges: Tyler Wallace’s Beginning Algebra and Intermediate Algebra, 2nd Edition: “Chapter 10, Section 10.5: Logarithmic Functions” (PDF)

Instructions: Read Section 10.5 in Chapter 10 of your textbook, pages 410–413, to learn about logarithmic functions. The logarithmic functions are the inverse functions to the exponential. Thus, these functions become important when needing to solve an exponential equation with the unknown in the exponent. Logarithmic functions have many real-world applications. When the magnitude of an earthquake is reported, the report does not give the actual tremor, since this is a very large number. The report gives the log of the tremor. The same is true for reporting sound (decibels) and acidity (ph). Note that this reading also covers the topics in Subunits 5.7.1–5.7.3.

Reading this section and taking notes should take approximately 2 hours.

• Assessment: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook: “Logs” Link: Big Bend Community College: Tyler Wallace’s Intermediate Algebra Lab Notebook“Logs” (PDF)

Instructions: Complete pages 112–114 of Wallace’s workbook. Try to complete this exercise before watching the videos in Subunits 5.7.1–5.7.3, and then review the worksheet as you follow along with the videos for solutions.

Completing this assessment should take approximately 1 hour.

5.7.1 Converting Logarithms   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.7.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Convert” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Convert” (YouTube)

Instructions: Watch the video linked above, which discusses how to convert from a logarithmic expression (log) to an exponential expression and vice versa. The conversion formula is: bx = a is equivalent to logba = x.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.7.2 Evaluating Logarithms   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.7.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Evaluate” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Evaluate” (YouTube)

Instructions: Watch the video linked above, which discusses evaluating logarithmic expressions. For general bases (bases other than 10 and e which are on all scientific calculators), determining the value of a log may be easier to convert to an exponential expression. Then you can use previous learned techniques to solve the exponential equation. Thus, convert logba = x to bx = a. Then use the techniques you learned in Subunit 5.5.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

5.7.3 Solving Logarithmic Equations   Note: This subunit is also covered by the reading and assessment assigned in Subunit 5.7.

• Lecture: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Solving” Link: YouTube: Tyler Wallace’s Math Lecture Series: “Logs – Solving” (YouTube)

Instructions: Watch the video linked above, which discusses solving logarithmic equations. As in the previous video, solving logarithmic equations is easier if first converted to an exponential equation.

You may watch the video as often as you please. You may refer to the video when doing the assessment if necessary.

Watching this video and pausing to take notes should take approximately 30 minutes.

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