Math Notes 7.3 Simplifying and Solving Exponential Functions 2024 PDF

Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook Section 7.3: Simplifying and Solving Exponential Expressions Simplifying Exponential Expressions (Using Law of Exponents) Review: Exponent Properties A. Negative Exponents a)...

Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook Section 7.3: Simplifying and Solving Exponential Expressions Simplifying Exponential Expressions (Using Law of Exponents) Review: Exponent Properties A. Negative Exponents a) b) c) Y ( = (1) 62. B. Zero Exponent a) b) 5 I C. Multiplication Rule a) 226 1 Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook D. Quotient Rule (5x 1) - - (3x - y a) 2 + 3 22x E. Power Rule = a) + 3 215x F. Rational Exponents and a) * 16 2 Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook Simplify Exponential Expressions write as a single base Example 1 Write the following expression with a single base. (a) [15x 21]5 - ↳ & L [(22)3x(23)3x +] - 7 5 25x - [26x 29x 21] - &. (b) 2x + 2 (53)x +1 2x 7 (52(3 g3x & 5 - -. - &. y (52)x +2 52x + + 3 gb 4x 33x -7 33x - - 2.. = 5 52x + y = + 2 5 (c) + 2x (23)x +2 (25)2x 14x + a.. = 2 */2 22x (13) x/2. 2 X b s 23x 2/0x + - L · + · 224 23x/2 =. 3  Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook Your Turn (c) ** F (2) (32(x +. (22)x 5 + 2 +Y (24* · (23)*. 22x E ((23)2)x +1 + y 22x I x 3+. + 3 = 12x + Y F 22x · 23. 2 +2 +y 22x 22x + y - · = E - - 3& E = 2 > + b 24x = 2 + E - 4 Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook Solving Exponential Equations Common Base Rule if and only if Example: +5 (3)x 3 = 3X + 15 3 3x + 15 = 4 3x = - 1) x - = 11/3 Common Exponent Rule < if and only if Example: (4 +) - 7 x = - 7 7 x - = y x = y Example 1 Solve for x (using like bases) (a) (b) T I 23x = 24 zx +2 = 9 3x = b x+2 3 = 32 x = 2 x +2 = 2 x = 0 5  Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook (c) d) ↑* + (22)2x (23)2x 3 9 (27)x - - = = X- = 9 (344x = 27 +x 2bx - 2 = X- = 38x = 27 4x 6x 9 E = - - 2x = - 9 38x (33) = x = I 2 38x 33 = x = 3 16X = 3x - 3 e) 13X = - 3 + x 3 (23(3x + (22)5x - = /3 = ((24)4)2x + 9x + 3 10 X-2 L = L - 32X - 16 L 10X -2 - 23x + 19 = 2 L 10X 2 23x + 19 - - = 21 = 33X = x 6 Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook (f) (3xte x (3 3) - = 3x - b y - 2x + 3 = 3 zX - 3x - 6 1x +5 - 3 = 3 1x + 5 = - 3x - b 4x = - 1) x = - I T (g) 2 [q)3x - x 49(7) = 2 ( +3)3x - (7)(7 = ) = Y 72-1x = 7 5 2 /X - = - 4 - S 6x 6 - 3x = - y 10 = 9X = x 7  Lesson 7.3 Simplifying and Solving Exponential Functions_2024.notebook h) Solve where ((32) tancy I co - COSX +0 = 3 / = CO - x + IL 32 E z 25, x - / 3 = 3 25inx = - Sinx = I 2 > Op = N R3 : F + = T 11 Q4 : 2 F - = To / i) Solve where (24)sinx = + sin x costx = 2 2 sink cosx 2 + 2451nx - = 4Sinx - 205x 1+ sinx six + 20 I = = cost = 1- si 4sinx - (1-sinx) = I + sinx 45inx-1 + / S sinx-1- Sin =0 =0 4sinx 2 & - + sinx = 2 PR = M↳ R1 : G Re : I = 5 8 T