Question

Find x such that 3^x+2 = 3^x + 216

Answer 1

Given 3^x+2 = 3^x + 216, 3^x+2 = 3^x + 216

Dividing throught by 3^x, we get

`(3^(x+2))/(3^x) = (3^x)/(3^x) + (2^3 + 3^3)/(3^x)`

3^x+2−x = 3^x−x + (2³ × 3^3−x)

3² = 3⁰ + 2³ × 3^3−x

3² − 3⁰ = 2³ × 3^3−x

9 − 1 = 2³ × 3^3−x 

8 = 2³ × 3^3−x 

`(2^3)/(2^3)` = 3^3−x 

2³⁻³ = 3^3−x

2⁰ = 3^3−x 

1 = 3^3−x 

3⁰ = 3^3−x  

Equating the powers of same base

0 = 3 − x

x = 3