For what value of x does 64 raised to the 3 x power is equal to 512 raised to the 2 x plus 12 power ?

Write both bases as powers of 2: 64 = 2^6 and 512 = 2^9. Then the equation becomes 2^(18x) = 2^(18x + 108), which would require 18x = 18x + 108. This is impossible, so there is no solution; the correct choice is “no solution.”

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