Module 6: Lesson 3

 

Self-Check 2

1. Questions 6, 7, and 12.c. on pages 380 and 381 of the textbook
   6.  
      1. In order for x to be a positive integer, x must be a value that is a positive power of 3. For example, x could be 3, 9, 27, 81, 243, ….
      2. In order for x to be a negative integer, x must be a value that is a negative power of 3. For example, x could be any of the following:
         
         
          
         
         
         This is because these values equate to 3−1, 3−2, 3−3, 3−4, ….
      3. In order for the value of log3 x to be equal to 0, x must be equal to 1.
      4. Answers will vary. Any value of x that is greater than 0 will provide a solution. However, only some of these are rational numbers. Some values that will work include the following:
         
         
          
         
   7.  
      1. The base of a logarithm cannot be 0 because, when converted to exponential form, this would leave a power with a base of 0. The result of 0 to any non-zero exponent would be 0, which would not create a logarithmic function.
      2. The base of a logarithm cannot be 1 because, when converted to exponential form, this would leave a power with a base of 1. The result of 1 to any exponent would be 1; which would not create a logarithmic function.
      3. The base of a logarithm cannot be negative because, when converted to exponential form, this would leave a power with a negative base. Exponential functions with bases that are negative do not form continuous functions and, thus, would not create a logarithmic function.

   12.  

       3. The equation can be solved in this way:
          
          
           
          

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