Solve for x:

\[ 64^{x-2} = 256^{2x} \]

6 4 x − 2 = 25 6 2 x ( 4 3 ) x − 2 = ( 4 4 ) 2 x 4 3 x − 6 = 4 8 x ⇔ 3 x − 6 = 8 x . 3 x − 8 x = 6 . − 5 x = 6 ⇔ x = − 5 6 ​

Answered by kate200468 | 2024-06-10

To solve the equation 6 4 x − 2 = 25 6 2 x , we rewrite both sides using the same base, leading to the equation 3 x − 6 = 8 x . Solving this gives us the final answer: x = − 5 6 ​ .
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Answered by kate200468 | 2025-01-14