1 College Algebra K/DC Friday, 08 April 2016 OBJECTIVE TSW solve exponential equations. Put assignment in wire basket, please ! QUIZ: Sec. 4.4 will be Monday, 04/11/16. TODAY’S ASSIGNMENT –Sec. 4.5: p. 464 (5-33 odd)  due on Tuesday, 04/12/16

Due Tuesday, 12 April Assignment: p. 446 (5-33 odd) Due Tuesday, 12 April Write each problem. Then solve each exponential equation. Express irrational solutions as decimals correct to the nearest thousandth (3 decimal places.) Use solution sets.

4-3 Exponential and Logarithmic Equations 4.5 Exponential Equations ▪ Logarithmic Equations

4-4 Remember? For all real numbers y and positive numbers a and x, where a ≠ 1, Product Property Quotient Property Power Property

4-5 Solve 8 x = 32. Solving an Exponential Equation What base is common to 8 and 32? Simplify. When the bases are the same, the exponents must be equal.

4-6 Solve 8 x = 21. Give the solution to the nearest thousandth (3 decimals). Solving an Exponential Equation Property of logarithms Power property Divide by ln 8. Solution set: {1.464} 8 and 21 do not have a common base.

4-7 Solve 5 2x–3 = 8 x+1. Give the solution to the nearest thousandth. Solving an Exponential Equation Solution set: {6.062} Property of logarithms Power property Distributive property Write the terms with x on one side. Factor.

4-8 Solve 5 2x–3 = 8 x+1. Give the solution to the nearest thousandth. Solving an Exponential Equation Do not round until the final answer!

4-9 Solve. Give the solution to the nearest thousandth. Solving Base e Exponential Equations Solution set: {±3.912} Property of logarithms ln e |x| = |x|

4-10 Solve. Give the solution to the nearest thousandth. Solving Base e Exponential Equations Solution set: {0.722} a m ∙ a n = a m + n Divide by e. Take natural logarithms on both sides. ≈ 0.722

4-11 Assignment Sec. 4.5: p. 446 (5-33 odd) –Write the problem and solve. Use solution sets. –Due Tuesday, 12 April 2016.

Due Tuesday, 12 April Assignment: p. 446 (5-33 odd) Due Tuesday, 12 April Write each problem. Then solve each exponential equation. Express irrational solutions as decimals correct to the nearest thousandth (3 decimal places.) Use solution sets.

13 College Algebra K/DC Monday, 11 April 2016 OBJECTIVE TSW solve exponential and logarithmic equations. QUIZ Sec. 4.4 will be tomorrow, Tuesday, 04/12/16. TODAY’S ASSIGNMENT (due Wed/Thurs, 04/13-14/16) –Sec. 4.5: p. 447 (35-59 odd)

4-14 Due on Wednesday/Thursday, 04/13-14/16 Assignment: Sec. 4.5: p. 447 (35-59 odd) Due on Wednesday/Thursday, 04/13-14/16. Write the problem and solve each equation, showing all work. Express all solutions in exact form. Use solution sets.

4-15 Exponential and Logarithmic Equations 4.5 Logarithmic Equations

4-16 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.

4-17 Solve log(2x + 1) + log x = log(x + 8). Give the exact value(s) of the solution(s). Solving a Logarithmic Equation Solution set: {2} Product property Distributive property Property of logarithms Solve the quadratic equation. The negative solution is not in the domain of log x in the original equation, so the only valid solution is x = 2. x must make these ALL of these arguments positive!

4-18 Solve. Give the exact value(s) of the solution(s). Solving a Logarithmic Equation Product property Subtract 8. Property of logarithms Multiply. Use the quadratic formula with a = 2, b = –11, and c = 7 to solve for x.

4-19 Solving a Logarithmic Equation The solution x = makes 2x – 5 in the original equation negative, so reject that solution. a = 2, b = −11, c = 7 Approximation: Exact Value:

4-20 Solve. Give the exact value(s) of the solution(s). Solving a Logarithmic Equation Solution set: {5} e ln x = x Quotient property Property of logarithms Multiply by x – 4. Solve for x.

4-21 Due before you leave today.  wire basket In-Class Problems: Sec. 4.5 Due before you leave today.  wire basket Write each problem, then solve each logarithmic equation. Express all solutions in EXACT FORM.

4-22 Due on Wednesday/Thursday, 04/13-14/16 Assignment: Sec. 4.5: p. 447 (35-59 odd) Due on Wednesday/Thursday, 04/13-14/16. Write the problem and solve each equation, showing all work. Express all solutions in exact form. Use solution sets.