Solve for \( y \).

\[ 8^3 - 3y = 256^{4y} \]

8 3 − 3 y = 25 6 4 y ( 2 3 ) 3 − 3 y = ( 2 8 ) 4 y 2 3 ( 3 − 3 y ) = 2 8 ⋅ 4 y 2 9 − 9 y = 2 32 y ⟺ 9 − 9 y = 32 y − 9 y − 32 y = − 9 − 41 y = − 9 / : ( − 41 ) y = 41 9 ​

Answered by Anonymous | 2024-06-10

To solve the equation 8 3 − 3 y = 25 6 4 y , convert all terms into base 2 and isolate y . After calculating, we find that the solution is y = 32 9 ​ . It's good to check both sides of the original equation for verification.
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Answered by Anonymous | 2024-12-26