1. Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 3.4: Solving Exponential and Logarithmic Equations Chapter 3 Test: Tues 12/15 and Wed 12/16 HW: p.217-218 (24, 26, 48-54 even, 58, 64, 68, 72, 74, 80)

2. 2 Properties One-to-One Properties 1.) If a x = a y, then x = y. 2.) If log a x = log a y, then x = y. Inverse Properties 3.) a log a x = x 4.) log a a x = x Because the domain of a logarithmic function generally does not include all real numbers, you should be sure to check for extraneous solutions of logarithmic equations.

3. 3 Solving Exponential Equations Solve each exponential equation and explain the process used to solve the equation. 1. e x = 722. 3(2 x ) = 42

4. 4 Solving Exponential Equations Solve each exponential equation and explain the process used to solve the equation. 3. 2(3 2t – 5 ) – 4 = 114. e 2x – 3e x + 2 = 0

5. 5 Solving Logarithmic Equations Solve each logarithmic equation and explain the process used to solve the equation. 1. ln 3x = 22. log 3 (5x – 1) = log 3 (x + 7)

6. 6 Solving Logarithmic Equations Solve each logarithmic equation and explain the process used to solve the equation. 3. 2log 5 3x = 44. ln(x – 2) + ln(2x – 3) = 2lnx

7. 7 Example 12 – Doubling an Investment You have deposited $500 in an account that pays 6.75% interest, compounded continuously. How long will it take your money to double?