If 2^(3x - 1) = 16^(x + 2), what is the value of x?
Show the answer and explanation
Correct answer
A. -9
Principle or equation
Express both sides with the same base. Since 16 = 2^4, rewrite 16^(x+2) as 2^(4(x+2)). Then equate exponents.
Why this answer is correct
2^(3x-1) = (2^4)^(x+2) = 2^(4x+8). Therefore 3x - 1 = 4x + 8, so x = -9.
Example
Solve 2^(x) = 8^(x-1). Since 8 = 2^3, x = 3(x-1) => x = 3/2.
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