Question

Find the value of x in the following:

3⁴⁰ + 3⁴⁰ + 3^x = 3⁴¹

Answer 1

Given, 3⁴⁰ + 3⁴⁰ + 3^x = 3⁴¹

Since, 3⁴⁰ + 3⁴⁰ + 3^x = 3⁴¹ 

⇒ 3^x = 3⁴¹ – 3⁴⁰ – 3⁴⁰

⇒ 3^x = 3⁴⁰3 – 1 – 1

⇒ 3^x = 3⁴⁰3 – 2

⇒ 3^x = 3⁴⁰

Equating the powers, we get

x = 40

Hence, the value of x is 40.