By definition of logarithm, logₓ(5/7) = −1/3 means x^(−1/3) = 5/7, i.e. x^(1/3) = 7/5. Cubing both sides: x = (7/5)³ = 343/125. Options (C) and (D) are negative and can be eliminated immediately because a positive base raised to any real power cannot give a negative result equal to 5/7 in the defining equation; (B) is the reciprocal of the correct answer, a common inversion error from mishandling the negative exponent. Hence (A) 343/125 is correct.
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