4^2x-1 - 16^x-1 = 384. find x
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4^(2x-1) - 16^(x-1) =384,
4^(2x-1) - [4²]^(x-1) =384,
4^(2x-1) - 4^(2x-2) =384,
4^(2x) [4^(-1) - 4^(-2)]=384,
4^(2x) [1/4 - 1/16] =384,
4^(2x) [4-1]/16 =384,
4^(2x) × 3/16 =384,
4^(2x) =384×16/3
4^(2x) =128×16,
4^(2x) =2048,
[2²]^(2x) =2¹¹,
2^(4x) =2¹¹,
therefore
4x=11,
x=11/4
4^(2x-1) - [4²]^(x-1) =384,
4^(2x-1) - 4^(2x-2) =384,
4^(2x) [4^(-1) - 4^(-2)]=384,
4^(2x) [1/4 - 1/16] =384,
4^(2x) [4-1]/16 =384,
4^(2x) × 3/16 =384,
4^(2x) =384×16/3
4^(2x) =128×16,
4^(2x) =2048,
[2²]^(2x) =2¹¹,
2^(4x) =2¹¹,
therefore
4x=11,
x=11/4
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