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Do Now 1/25/19 Copy HW in your planner. Text p. 329, #4-30 evens, 38, 40, 44, 46, 54, 56, 58 Chapter 6 Test – Wenesday, January 29th If you did not finish the quiz from yesterday, get your scrap paper and complete the rest of the quiz. Once you finish the quiz, or if you finished the quiz yesterday, complete the notes and examples in the following slides.

Learning Goal Learning Target SWBAT simplify, graph, and solve exponential expressions, equations, functions and sequences. Learning Target SWBAT solve exponential equations with the same base, unlike bases, and by graphing

Section 6.5 “Solving Exponential Equation” equation in which variable expressions occur as exponents. If 2x = 25 then x is equal to 5. Two powers with the same positive base b are equal if their exponents are equal.

Solving Exponential Equations with the Same Base Since the bases are the same, then in order to solve for x, write an equation for the exponents. Since the bases are the same, then in order to solve for x, write an equation for the exponents. 3x+1 = 35 81 = 82x-3

On Your Own Solving Exponential Equations with the Same Base 102x+1 = 103x 5x+1 = 53x+5 Since the bases are the same, then in order to solve for x, write an equation for the exponents. Since the bases are the same, then in order to solve for x, write an equation for the exponents. 5x+1 = 53x+5 102x+1 = 103x

Solving Exponential Equations with Unlike Bases 4x = 23x-4 Since the bases are unlike, rewrite 64 as a power of 4. Since the bases are unlike, rewrite 4x as a power of 2. (22)x = 23x-4 4x = 43 22x = 23x-4 Then, write and solve an equation for the exponents. Then, write and solve an equation for the exponents. 4x = 43 22x = 23x-4

On Your Own Solving Exponential Equations with Unlike Bases 92x = 3x-6 43x = 8x+1 Since the bases are unlike, rewrite 92x as a power of 3. Since the bases are unlike, rewrite 43x as a power of 8. (32)2x = 3x-6 (43)x = 8x+1 64x = 8x+1 34x = 3x-6 82x = 8x+1 Then, write and solve an equation for the exponents. Then, write and solve an equation for the exponents. 34x = 3x-6 82x = 8x+1

Solving Exponential Equations with Unlike Bases when 0 < b < 1 Since the bases are unlike, rewrite both expressions as common bases. 2-1x = 24 Then, write and solve an equation for the exponents. 2-1x = 24 x = -4

4x+1 = 4-3 3-x+1 = 33 4x+1 = 1/64 (1/3)x-1 = 27 4x+1 = 4-3 On Your Own Solving Exponential Equations with Unlike Bases when 0 < b < 1 4x+1 = 1/64 (1/3)x-1 = 27 Since the bases are unlike, rewrite both expressions as common bases. Since the bases are unlike, rewrite 1/64 as a power of 4. (3-1)x-1 = 33 4x+1 = 4-3 (3)-1(x-1) = 33 Then, write and solve an equation for the exponents. 3-x+1 = 33 Then, write and solve an equation for the exponents. 4x+1 = 4-3 3-x+1 = 33

Solving Exponential Equations by Graphing. Sometimes, it is impossible to rewrite each side of an exponential equation using the same base. You can solve these types of equations by GRAPHING EACH SIDE and finding the point of intersection. Use the INTERSECT feature on your calculator to find the point of intersection. 2nd CALC 5: intersect ENTER The solution is the “x” value of the ordered pair.

On Your Own Solving Exponential Equations by Graphing. 2nd CALC 5: intersect ENTER No solution because the graphs do not intersect.

Homework Text p. 329, #4-30 evens, 38, 40, 44, 46, 54, 56, 58