To solve the given equation logx(5/7) = -1/3, we need to understand the properties of logarithms and how to manipulate them.

1. The logarithm of a fraction can be expressed as the difference of the logarithms of the numerator and the denominator.

2. The logarithm of a number raised to a power can be expressed as the product of the power and the logarithm of the number.

Using these properties, let's solve the equation step by step:

Step 1: Express the given equation using the properties of logarithms.
logx(5/7) = logx(5) - logx(7)

Step 2: Since logx(5/7) = -1/3, we can rewrite the equation as:
-1/3 = logx(5) - logx(7)

Step 3: Now, let's express the logarithms in terms of the base x.
-1/3 = logx(5) - logx(7)
-1/3 = logx(5) - 1/logx(7)

Step 4: Multiply both sides of the equation by 3 to eliminate the fraction.
-1 = 3 * (logx(5) - 1/logx(7))

Step 5: Distribute 3 to both terms inside the parentheses.
-1 = 3 * logx(5) - 3 * (1/logx(7))

Step 6: Simplify the expression.
-1 = 3 * logx(5) - 3/logx(7)

Step 7: Let's focus on the second term, -3/logx(7).
To simplify it further, we can express -3 as -3/1 and multiply it by logx(7)/logx(7).

-1 = 3 * logx(5) - (3 * logx(7))/logx(7)

Step 8: Combine the terms with the same denominators.
-1 = (3 * logx(5) * logx(7) - 3 * logx(7))/logx(7)

Step 9: Combine the terms in the numerator.
-1 = (3 * (logx(5) * logx(7) - logx(7)))/logx(7)

Step 10: Simplify the expression further.
-1 = (3 * logx(5 * 7))/logx(7)

Step 11: Simplify the numerator.
-1 = (3 * logx(35))/logx(7)

Step 12: Since the bases of the logarithms are the same, the numerators must be equal.
3 * logx(35) = -1

Step 13: Divide both sides of the equation by 3.
logx(35) = -1/3

Step 14: Comparing the equation with the given equation, we can conclude that x = 35.

Therefore, the correct answer is option A) 343/125.