Question

Solve the following equation:

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

Answer 1

Given equation: `2^(4x - 3) = 4 xx 2^(2x - 1)`

Step-wise calculation:

1. Rewrite 4 as a power of 2:

4 = 2², so the equation becomes:

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

2. Using the property of exponents a^m × aⁿ = a^{m + n}, rewrite the right side:

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

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

3. Since the bases are equal, equate the exponents:

4x – 3 = 2x + 1

4. Solve for (x):

4x – 2x = 1 + 3 

⇒ 2x = 4

⇒ x = 2