Question

Solve the following equation:

`2^(4x + 1) = root(4)(256)`

Answer 1

Given: `2^(4x + 1) = root(4)(256)`

Step-wise calculation:

1. Express 256 as a power of 2:

256 = 2⁸

2. Rewrite the right side using the 4th root:

`root(4)(256) = (2^8)^(1/4)`

`root(4)(256) = 2^(8 xx 1/4)`

`root(4)(256) = 2^2`

3. Equate the powers of 2 on both sides:

`2^(4x + 1) = 2^2`

4. Since the bases are the same, set the exponents equal:

4x + 1 = 2

5. Solve for (x):

4x = 2 – 1

4x = 1 

⇒ `x = 1/4`