1. Lesson 6

1.1. Discover

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

Discover
 

There are many applications of exponential and logarithmic functions. In most cases, the expressions in the equations are difficult to write in the same base, so you need to find a way to solve these equations algebraically. In Try This 1 you will review how to solve equations with the same base. Later in the lesson you will learn how to solve equations that can’t be easily rewritten with the same base.

 

Try This 1

 

Use the equation 2 log x = log 25 to answer the following questions.

  1. Apply the power law of logarithms to the left side of the equation.
  2. Explain how you can solve the resulting equation algebraically.
  3. Determine two values of x that satisfy the equation from question 2. Are both solutions valid?
  4. Describe how you can solve the equation graphically.
  5. Use your method to solve the equation graphically.1

course folder Save your responses in your course folder.


Share 1

 

With a partner or group, compare your answers from questions 3 and 5 of Try This 1. Explain any differences.

 

course folder If required, save a record of your discussion in your course folder.

 

1 Adapted from Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.

When solving exponential equations when the bases of the powers are the same on each side of the equation, the exponents are equal. For example, if 2x−1 = 23, then x − 1 = 3. Could this idea be used with logarithms?