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## 2.1, 6.7 Exponential Equations

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**2.1, 6.7 Exponential Equations**OBJ: To solve an exponential equation To solve an exponential equation using properties of rational number exponents**EX: 5 8 x = 16**P15823x = 24 3x = 4 x = 4/3 EX: 9 x = 27 32x = 33 2x = 3 x = 3/2 EX: (1/3) x = 9 3-x = 32 -x = 2 x = -2 EX: (3/4) x = 16/9 (3/4) x = (3/4)-2 x = -2 DEF: Exponential EquationGet same bases; set exponents =**EX: 6 (5) 4x + 1 = 125**P 33(5) 4x + 1 = 5 3 4x + 1 = 3 x = 1/2 EX: (3) 2x + 4 = 243 32x + 4 = 35 2x + 4 = 5 x = 1/2 EX: (8) 4z = (4) z + 1 (23)4z = (22) z + 1 12 z = 2z + 2 10z = 2 z = 1/5 EX: (64) t = (32) 1 - t (2 6) t = (2 5) 1- t 6 t = 5 – 5t t = 5/11**EX: 625 –x = 125 3 x**(54) –x = (53) 3x - 4x = 9x 0 = 13x 0 = x EX: 125 3 – a = 25 a (5 3) 3 – a = (5 2) a 9 – 3a = 2a 9 = 5a 9/5 = a EX: (1/27)– 2 p=(3)p+3 (3- 3)– 2 p = (3)p+3 6p = p + 3 5p = 3 p = 3/5 EX: 2 – h = (1/8) 1 – h 2 – h = (2 - 3) 1 – h - h = - 3 + 3h - 4h = - 3 h = 3/4 EX: (1/3) – x = (1/9) x + 1 (1/3) – x = [(1/3)2]x + 1 -x = 2x + 2 -3x = 2 x = -2/3 EX: 2 – x = 1/8 2 – x = 2 -3 - x = -3 x = 3 x = 3, -3