College Algebra K /DC Wednesday, 09 April 2014

1. College Algebra K/DCWednesday, 09 April 2014 • OBJECTIVETSW solve exponential equations. • ASSIGNMENT DUE • Sec. 4.4: pp. 453-454 (29-42 all, 45-50 all) wire basket • Sec. 4.4: pp. 455-457 (53-56 all, 61-72 all) black tray • QUIZ FRIDAY • Sec. 4.4 • TEST: Sec. 4.1 – 4.3 will be given back at 1:45.

2. Exponential and Logarithmic Equations 4.5 Exponential Equations ▪ Logarithmic Equations

3. Remember? For all real numbers yand positive numbers a and x, where a ≠ 1, Product Property Quotient Property Power Property

4. Solving an Exponential Equation • Solve 8x = 32. What base is common to 8 and 32? Simplify. When the bases are the same, the exponents must be equal.

5. Solving an Exponential Equation • Solve 8x = 21. Give the solution to the nearest thousandth (3 decimals). 8 and 21 do not have a common base. Property of logarithms Power property Divide by ln 8. Solution set: {1.464}

6. Solving an Exponential Equation Property of logarithms Power property Distributive property Write the terms with x on one side. Factor. • Solve 52x–3 = 8x+1. Give the solution to the nearest thousandth. Solution set: {6.062}

7. Solving an Exponential Equation • Solve 52x–3 = 8x+1. Give the solution to the nearest thousandth. Do not round until the final answer!

8. Solving Base e Exponential Equations Property of logarithms ln e|x| = |x| • Solve . Give the solution to the nearest thousandth. Solution set: {±3.912}

9. Solving Base e Exponential Equations am∙ an= am + n Divide by e. Take natural logarithms on both sides. • Solve . Give the solution to the nearest thousandth. Solution set: {0.722} ≈ 0.722

10. Assignment • Sec. 4.5: p. 464 (5-27 odd) • Write the problem and solve. Use solution sets. • Due on Friday, 11 April 2014.

11. Assignment: p. 464 (5-27 odd)Due on Friday, 11 April 2014. • Write each problem. Then solve each exponential equation. Express irrational solutions as decimals correct to the nearest thousandth (3 decimal places.)

12. Exponential and Logarithmic Equations 4.5 Logarithmic Equations

13. Logarithmic Equations • Logarithms have restrictions: • base: > 0≠ 1 • argument: > 0 • (The exponent has no restrictions.) • When you solve logarithmic equations, you must (at least mentally) check your solutions to see if they satisfy the restrictions.

14. Solving a Logarithmic Equation Product property Distributive property Property of logarithms Solve the quadratic equation. • Solve log(2x + 1) + log x = log(x + 8). Give the exact value(s) of the solution(s). x must make these ALL of these arguments positive! The negative solution is not in the domain of log x in the original equation, so the only valid solution is x = 2. Solution set: {2}

15. Solving a Logarithmic Equation Product property Property of logarithms Multiply. Subtract 8. • Solve . Give the exact value(s) of the solution(s). Use the quadratic formula with a = 2, b = –11, and c = 7 to solve for x.

16. Solving a Logarithmic Equation a = 2, b = −11, c = 7 Approximation: Exact Value: The solution x = 0.734 makes 2x – 5 in the original equation negative, so reject that solution.

17. Solving a Logarithmic Equation eln x= x Quotient property Property of logarithms Multiply by x – 4. Solve for x. • Solve . Give the exact value(s) of the solution(s). Solution set: {5}

18. Assignment • Sec. 4.5: pp. 464-465 (29-51 odd) • Write the problem and solve; use solution sets. • Due on Wednesday, 16 April 2014 (TEST day).

19. Assignment: Sec. 4.5: pp. 464-465 (29-51 odd)Due on Wednesday, 16 April 2014 (TEST day). • Write the problem and solve each equation, showing all work. Express all solutions in exact form. Use solution sets.