If z = 0 . 0064 , find the value of 1 z 1 / 2 .

Given, z = 0 . 0064 ⇒ 1 z 1 2 = 1 0 . 0064 1 2 = 10000 64 1 2 = 100 2 8 2 1 2 = 100 8 2 1 2 = 100 8 2 × 1 2 = 100 8 = 25 2 = 12 . 5

If 81 x = 9 3 x , find the value of x .

Given 81 x = 9 3 x ⇒ 3 4 x = 3 2 3 x ⇒ 3 4 x = 3 2 - x ⇒ 4 x = 2 - x ⇒ 4 x + x = 2 ⇒ 5 x = 2 ⇒ x = 2 5

Find the value of x , if 2 9 x ÷ 2 2 x = 2 14 7 .

Given, 2 9 x ÷ 2 2 x = 2 14 7 ⇒ 2 9 x 2 2 x = 2 14 1 7 ⇒ 2 9 x - 2 x = 2 14 × 1 7 ⇒ 2 7 x = 2 2 ⇒ 7 x = 2 ⇒ x = 2 7

Prove that 2 30 + 2 29 + 2 28 2 31 + 2 30 - 2 29 = 7 10 ,

Given expression is 2 30 + 2 29 + 2 28 2 31 + 2 30 - 2 29 = 2 28 + 2 + 2 28 + 1 + 2 28 2 28 + 3 + 2 28 + 2 - 2 28 + 1 = 2 28 × 2 2 + 2 28 × 2 1 + 2 28 × 1 2 28 × 2 3 + 2 28 × 2 2 - 2 28 × 2 1 = 2 28 × 4 + 2 28 × 2 + 2 28 × 1 2 28 × 8 + 2 28 × 4 - 2 28 × 2 = 2 28 4 + 2 + 1 2 28 8 + 4 - 2 = 4 + 2 + 1 8 + 4 - 2 = 7 10

Find the value of 3 2 4 5 .

We are required to find the value of 3 2 4 5 = 3 2 4 1 5 = 3 2 1 4 1 5 = 3 2 × 1 4 1 5 = 3 1 2 1 5 = 3 1 2 × 1 5 = 3 1 10 = 3 10

Find the value of 2 2 3 4 .

We are required to simplify 2 2 3 4 = 2 2 3 1 4 = 2 2 1 3 1 4 = 2 2 × 1 3 1 4 = 2 2 3 1 4 = 2 2 3 × 1 4 = 2 1 6 = 2 6

If a = 2 x - 1 2 x - 2 , b = 2 - x 2 x + 1 and a - b = 0 , find the value of x .

Given a = 2 x - 1 2 x - 2 , b = 2 - x 2 x + 1 Now a = 2 x - 1 2 x - 2 = 2 x - 1 - x - 2 = 2 x - 1 - x + 2 ∴ a = 2 Also, b = 2 - x 2 x + 1 = 2 - x - x + 1 = 2 - x - x - 1 = 2 - 2 x - 1 Now, a - b = 0 ⇒ 2 - 2 - 2 x - 1 = 0 ⇒ 2 1 = 2 - 2 x - 1 ⇒ 1 = - 2 x - 1 ⇒ 2 x = - 2 ⇒ x = - 1

E M B I B E

All in One Mathematics>Chapter 1 - Number Systems>Exercise 1.4

Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Number Systems, Exercise 4: Exercise 1.4

Author:Brijesh Dwevedi & Jitendra Gupta

Brijesh Dwevedi Mathematics Solutions for Exercise - Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Number Systems, Exercise 4: Exercise 1.4

Attempt the practice questions on Chapter 1: Number Systems, Exercise 4: Exercise 1.4 with hints and solutions to strengthen your understanding. All in One Mathematics solutions are prepared by Experienced Embibe Experts.