Student: Class: Date: Solving equations and inequalities Student Activity Sheet 3; use with Exploring “Analytic techniques” 1. Use logarithms to solve the equation shown. (Hint: Divide both sides of the equation by one of the constants—either 16,000 or 20,000.) 20,000(0.92)t = 16,000(0.93)t Copyright 2011 Agile Mind, Inc.  Content copyright 2011 Charles A. Dana Center, The University of Texas at Austin Page 1 of 5 With space for student work Student: Class: Date: Solving equations and inequalities Student Activity Sheet 3; use with Exploring “Analytic techniques” 2. Using the steps provided, fill in the table to show the correct order for solving the equation 23x = 3x + 6. Evaluate the expression for x. Apply the power property for logs. Collect like terms by subtracting. Divide each side by the coefficient of x. Factor out x. Distribute to clear any parentheses. Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Copyright 2011 Agile Mind, Inc.  Content copyright 2011 Charles A. Dana Center, The University of Texas at Austin Page 2 of 5 With space for student work Take the log of both sides. Student: Class: Solving equations and inequalities Student Activity Sheet 3; use with Exploring “Analytic techniques” 3. Solve the equation 23x = 3x + 6. 4. R REEIINNFFOORRCCEE Solve the equation 63x-2 = 5x+1. 5. Isolate the logarithm in the equation shown. 10 ln 100x – 3 = 117 6. After isolating the logarithm in question 5, solve for x. Copyright 2011 Agile Mind, Inc.  Content copyright 2011 Charles A. Dana Center, The University of Texas at Austin Page 3 of 5 With space for student work Date: Student: Class: Date: Solving equations and inequalities Student Activity Sheet 3; use with Exploring “Analytic techniques” 7. Complete the following table to investigate how e and ln are related. (Hint: Do not round your values for ln x before evaluating eln x.) x 0.1 ln x -2.3025 0.2 0.5 1 2 e 10 eln x 8. What does eln x appear to equal? Why does this make sense? 9. Use eln x = x to help you solve the equation shown. ln x = ln(2x + 2) 10. Is the answer you found in question 9 a solution to the equation ln x = ln(2x + 2)? Why or why not? Copyright 2011 Agile Mind, Inc.  Content copyright 2011 Charles A. Dana Center, The University of Texas at Austin Page 4 of 5 With space for student work Student: Class: Date: Solving equations and inequalities Student Activity Sheet 3; use with Exploring “Analytic techniques” 11.R REEIINNFFOORRCCEE Solve the following equation analytically, and then verify your solution using a table and graph. 12.R REEIINNFFOORRCCEE Solve the following equation analytically, and then verify your solution using a table and graph. Copyright 2011 Agile Mind, Inc.  Content copyright 2011 Charles A. Dana Center, The University of Texas at Austin Page 5 of 5 With space for student work