Chapter 8-5 Exponential and Logarithmic Equations Day 1: Exponential Equations

1. Chapter 8-5Exponential and Logarithmic EquationsDay 1: Exponential Equations Essential Question: Give examples of equations that can be solved using the properties of exponents and logarithms.

2. 8-5: Exponential and Logarithmic Equations • An equation where the exponent is a variable is an exponential equation. • You solve exponential equations by converting them into logarithmic equations, and using the properties of logarithms to simplify. • As a rule:you need to get the base and exponent alone on one side of the equation first before converting to a log.

3. 8-5: Exponential and Logarithmic Equations • Example • Solve 73x = 20 log7 20 = 3x convert to logchange of base formuladivide both sides by 30.5132 = x use calculator round to 4 decimal places

4. 8-5: Exponential and Logarithmic Equations • Example (get base/exponent alone first) • Solve 5 - 3x = -40 -3x = -45 subtract 5 on both sides3x = 45 divide both sides by -1 log3 45 = x convert to logchange of base formula 3.4650 = x use calculator round to 4 decimal places

5. 8-5: Exponential and Logarithmic Equations • Your Turn • Solve 3x = 4 • Solve 62x = 21 • Solve 3x+4 = 101 1.2619 0.8496 0.2009

6. 8-5: Exponential and Logarithmic Equations • Assignment • Page 464 • Problems 1 – 19 (odds) • Show your work, and round your answers to 4 decimal places • Ignore the directions about solving by graphing and using a table.

7. Chapter 8-5Exponential and Logarithmic EquationsDay 2: Logarithmic Equations Essential Question: Give examples of equations that can be solved using the properties of exponents and logarithms.

8. 8-5: Exponential and Logarithmic Equations • An equation that includes a logarithmic expression, such as log3 15 = log2 x is called a logarithmic equation. • You solve logarithmic equations by using the properties of logarithms to simplify and then converting them into exponential equations. • As a rule:you need to get the logs on one side of the equation and combined into only one log before converting to an exponential equation. • As another rule: If there is no base on a logarithmic problem, we assume the base is 10

9. 8-5: Exponential and Logarithmic Equations • Example • Solve log (3x + 1) = 5 Only one log? Check log10 (3x + 1) = 5 Assume base 10 105 = 3x + 1 Convert to exponential form 100,000 = 3x + 1 Simplify left side 99,999 = 3x Subtract 1 from both sides 33,333 = x Divide both sides by 3

10. 8-5: Exponential and Logarithmic Equations • Example (combining logs first) • Solve 2 log x – log 3 = 2 log x2 – log 3 = 2 Power ruleQuotient RuleOnly one log? CheckAssume base 10 102 = Convert to exponential form 100 = Simplify left side 300 = x2Multiply both sides by 3 17.3205 = x Square root both sides

11. 8-5: Exponential and Logarithmic Equations • Your Turn • Solve log (7 – 2x) = -1 • Solve log (2x – 2) = 4 • Solve 3 log x – log 2 = 5 • Solve log 6 – log 3x = -2 3.45 5001 58.4804 200

12. 8-5: Exponential and Logarithmic Equations • Assignment • Page 464 - 465 • Problems 33 – 47 (odds) • Show your work, and round your answers to 4 decimal places (if necessary) • Ignore the directions about solving by graphing and using a table.