If log x (1/343) = -3, then the value of x is equal to:

Concept: A logarithmic statement logb(N) = k is defined only when the base b is positive and b ≠ 1, and by definition it means bk = N.

Application:

1. Given logx (1/343) = -3, applying the definition gives x-3 = 1/343.

2. x-3 = 1/x3, so 1/x3 = 1/343, which gives x3 = 343.

3. Taking the cube root of both sides: x = 7.

Cross-check: 7-3 = 1/73 = 1/343, matching the given value. A logarithm's base must also be positive and not equal to 1, so x = 7 is the only valid solution — 7 is positive, confirming it fits the base condition.