PreCalculus Honors 3 4 Solving Exponential and Logarithmic

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) Copyright © Cengage Learning. All rights reserved.

Properties One-to-One Properties 1. ) If ax = ay, then x = y. 2. ) If loga x = loga y, then x = y. Inverse Properties 3. ) aloga x = x 4. ) loga ax = 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. 2

Solving Exponential Equations Solve each exponential equation and explain the process used to solve the equation. 1. ex = 72 2. 3(2 x) = 42 3

Solving Exponential Equations Solve each exponential equation and explain the process used to solve the equation. 3. 2(32 t – 5) – 4 = 11 4. e 2 x – 3 ex + 2 = 0 4

Solving Logarithmic Equations Solve each logarithmic equation and explain the process used to solve the equation. 1. ln 3 x = 2 2. log 3(5 x – 1) = log 3(x + 7) 5

Solving Logarithmic Equations Solve each logarithmic equation and explain the process used to solve the equation. 3. 2 log 53 x = 4 4. ln(x – 2) + ln(2 x – 3) = 2 lnx 6

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? 7