Question

Solve the following equation:

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

Answer 1

Given equation: `2^(3x + 1) = 16 xx 2^(2x)`

Step-wise calculation:

1. Express 16 as a power of 2:

16 = 2⁴ 

So the equation becomes:

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

2. Use the property of exponents:

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

Hence: `2^(3x + 1) = 2^(4 + 2x)`.

3. Since the bases are the same and nonzero, equate the exponents:

3x + 1 = 4 + 2x

4. Solve for (x):

3x + 1 = 4 + 2x

3x – 2x = 4 – 1

x = 3