If 2ˣ = 4ˣ⁻¹, find x.
2
Given \(2^x = 4^{x-1}\).
Rewrite 4 as a power of 2: \(4^{x-1} = (2^2)^{x-1} = 2^{2(x-1)} = 2^{2x-2}\).
So the equation becomes \(2^x = 2^{2x-2}\).
Since the bases are equal, the exponents must be equal: \(x = 2x - 2\).
Solving, \(2x - x = 2 \Rightarrow x = 2\).
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