Indices (Assignment #1)

University:
Stanford University
Course:
Introduction to Mathematical Thinking
Academic year:

2023
Views:

490

Pages:

3
Author:

MAlphen

Indices 1 (a) 3𝑝 = 35 + 35 + 35. Find the value of p. 0 𝑥4×(2𝑥3) ×√𝑥 (b) Simplify [1] , giving your answer in positive index. −1 2𝑥 (c) Solve the equation 52𝑞−1 1 = . [3] [2] 625 1 2 (a) Simplify (5𝑥)3 × (9𝑦4)−2, leaving your answer in positive index notation. 2𝑦 (b) Solve 6 ×36 = 216𝑦. 1 [3] [3] 63 1 3 (a) Solve 4𝑥 = [2] . 32 3 𝑛 [3] −2 (b) Simplify 𝑚2𝑛−5 ÷ ( ) , giving your answer in positive index notation. 𝑚 1 Solutions: (a) 𝑝 = 1 + 5 = 6 (b) 𝑥4×(2𝑥3)0×√𝑥 2𝑥−1 1 2𝑞−1 (c) 5 = 625 = 𝑥4×1×𝑥2 = 5−4 2 𝑥 9 2 1 𝑥 1 11 2 = 𝑥 × 2 = 2𝑥 2𝑞 − 1 = −4 𝑞 = −1.5 11 Ans: (a) 6 (b) 1 𝑥 2 (c) 𝑞 = −1.5 2 2 Solutions: (a) (5𝑥)3 × =125𝑥3 × = 125𝑥3 × = 125𝑥3 2𝑦 1 (9𝑦4)2 1 (b) 6 6 1 (9𝑦4)2 3𝑦2 3𝑦2 3 Ans: (a) 125𝑥 (b) 𝑦 = 1 3𝑦2 2 3 ×36 1 3 6 2𝑦 = 216𝑦 ×62 1 63 = 63𝑦 By1comparing powers, 1 2𝑦 + 2 − 3 = 3𝑦 2 𝑦=1 3 3 Solutions: (a) 4𝑥 = 1 32 22𝑥 = 2−5 2𝑥 = −5 ∴ 𝑥 = −2.5 3 𝑛 (b) 𝑚2𝑛−5 ÷ ( ) −2 𝑚 2 −5+2 𝑛 𝑛 2 3 = 𝑚2𝑛−5 × ( ) 𝑚 3 = 𝑚2 1 = 𝑚2𝑛−3 1 = 1 𝑚2𝑛3 Ans: (a) 𝑥 = −2.5 (b) 1 𝑚2𝑛3 1