Question

if 2^x-1 + 2^x+1 = 2560, find x it will be 10, please solve

Answer 1

◐ Given ◐

• 2ˣ ⁻ ¹ + 2ˣ ⁺ ¹ = 2560

◐ To find ◐

• x

◐ Solution ◐

• 2ˣ ⁻ ¹ + 2ˣ ⁺ ¹ = 2560
• 2ˣ.2⁻¹ + 2ˣ.2¹ = 2560
• 2ˣ (2⁻¹ + 2¹) = 2560
• 2ˣ (½ + ²⁄₁) = 2560
• 2ˣ  (⁵⁄₂) = 2560
• 2ˣ  = 2560 × ⅖
• 2ˣ = 1024
• 2ˣ = 2¹⁰
• x = 10

∅ Value of x is 10

◐ Laws of exponents ◐ (Used in the solution)

• a⁻ⁿ = 1/n
• aᵐ × aⁿ = aᵐ ⁺ ⁿ
• aᵐ = aᵐ = a = a
• aᵐ ⁻ ⁿ = aᵐ.aⁿ

Answer 2

Answer:

◐ Given ◐

2ˣ ⁻ ¹ + 2ˣ ⁺ ¹ = 2560

◐ To find ◐

x

◐ Solution ◐

2ˣ ⁻ ¹ + 2ˣ ⁺ ¹ = 2560

2ˣ.2⁻¹ + 2ˣ.2¹ = 2560

2ˣ (2⁻¹ + 2¹) = 2560

2ˣ (½ + ²⁄₁) = 2560

2ˣ  (⁵⁄₂) = 2560

2ˣ  = 2560 × ⅖

2ˣ = 1024

2ˣ = 2¹⁰

x = 10

∅ Value of x is 10

◐ Laws of exponents ◐ (Used in the solution)

a⁻ⁿ = 1/n

aᵐ × aⁿ = aᵐ ⁺ ⁿ

aᵐ = aᵐ = a = a

aᵐ ⁻ ⁿ = aᵐ.aⁿ