Question

Find the value of x if 9²⁰ + 9²⁰ + 9²⁰ = 3^x

Answer 1

We are solving:

9²⁰ + 9²⁰ + 9²⁰ = 3^x

Step 1: Combine like terms

9²⁰ + 9²⁰ + 9²⁰ = 3 · 9²⁰

Step 2: Express in terms of base 3

9 = 3²

⇒ 9²⁰ = (3²)²⁰ = 3⁴⁰

So, 3 · 9²⁰ = 3 · 3⁴⁰

Step 3: Apply exponent laws

3 · 3⁴⁰ = 3¹ · 3⁴⁰ = 3⁴¹

x = \[\boxed{41}\]