For what value of x does 4 to the x th power is equal to 1 eighth raised to the x plus 5 power ?

Rewrite both sides using base 2: 4^x = 2^(2x), and (1/8)^(x+5) = 2^[-3(x+5)]. Since the bases are equal, set the exponents equal: 2x = -3x - 15. Solving gives 5x = -15, so x = -3, choice A, negative 3.

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