Question

If `3^(3x + 1) = 3^(3x - 1) + 72`, find the value of `(3x + 1)^(2x)`.

Answer 1

Given: `3^(3x + 1) = 3^(3x - 1) + 72`

Step-wise calculation:

1. Rewrite the equation as:

`3^(3x + 1) - 3^(3x - 1) = 72`

2. Factor out `3^(3x - 1)`:

`3^(3x - 1) (3^2 - 1) = 72`

`3^(3x - 1)(9 - 1) = 72`

`3^(3x - 1) xx 8 = 72`

3. Divide both sides by 8:

`3^(3x - 1) = 72/8`

`3^(3x - 1) = 9`

4. Since 9 = 3², 

`3^(3x - 1) = 3^2`

⇒ 3x – 1 = 2

⇒ 3x = 3

⇒ x = 1

5. Calculate `(3x + 1)^(2x)`:

`(3 xx 1 + 1)^(2 xx 1) = 4^2`

`(3 xx 1 + 1)^(2 xx 1) = 16`