Question

Find the value of x in the following:

4²⁰ + 4²⁰ = 2^x

Answer 1

Given, 4²⁰ + 4²⁰ = 2^x

Since, 4²⁰ + 4²⁰ = 2^x = 4²⁰(1 + 1) = 2^x

⇒ 4²⁰ × (2) = 2^x

⇒ (2²)²⁰ × 2¹ = 2^x

⇒ (2)⁴⁰ × 2¹ = 2^x   ...[∵ a^m × aⁿ = a^{m + n}]

⇒ (2)⁴¹  

⇒ 2^x

∴ x = 41