2.1, 6.7 Exponential Equations

OBJ: To solve an exponential

equation

To solve an exponential

equation using properties of rational

number exponents

DEF: Exponential EquationGet same bases; set exponents =EX: 5 8 x = 16P158 23x = 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

EX: 6 (5) 4x + 1 = 125P 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 = 1/5EX: (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 = xEX: 125 3 – a = 25 a (5 3) 3 – a = (5 2) a

9 – 3a = 2a 9 = 5a

9/5 = aEX: (1/27)– 2 p=(3)p+3

(3- 3)– 2 p = (3)p+3

6p = p + 35p = 3p = 3/5

EX: 2 – h = (1/8) 1 – h

2 – h = (2 - 3) 1 – h

- h = - 3 + 3h - 4h = - 3

h = 3/4EX: (1/3) – x = (1/9) x + 1 (1/3) – x = [(1/3)2]x + 1

-x = 2x + 2 -3x = 2

x = -2/3EX: 2 – x = 1/8

2 – x = 2 -3

- x = -3 x = 3

x = 3, -3