If 4^(x - 1) = 8^(2x + 1), what is the value of x?
Show the answer and explanation
Correct answer
A. -5/4
Principle or equation
Express both sides with the same base and equate exponents.
Why this answer is correct
4 = 2^2, 8 = 2^3. So 2^(2(x - 1)) = 2^(3(2x + 1)). Equate exponents: 2x - 2 = 6x + 3 → -4x = 5 → x = -5/4.
Example
Solve 9^(x) = 27^(x - 1): 3^(2x) = 3^(3x - 3) → 2x = 3x - 3 → x = 3.
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