To solve this logarithmic equation, we first need to simplify both sides of the equation.

Using the properties of logarithms, we can rewrite the left side of the equation as a single logarithm:

log_100((25-2x)/(75-7x)) = 3 - log_81(3^81)

Now we need to convert both sides of the equation to a common base. Let's convert everything to base 10, as it is commonly used:

(log((25-2x)/(75-7x)) / log(100)) = 3 - (log(3^81) / log(81))

Simplifying further:

(log((25-2x)/(75-7x)) / 2) = 3 - (81 * log(3) / 4)

Now let's simplify the left side:

log((25-2x)/(75-7x)) = 6 - (81/4) * log(3)

Now we can express the equation in exponential form:

(25-2x)/(75-7x) = 10^(6 - (81/4) * log(3))

Now solve for x by isolating x on one side of the equation. This may involve some algebraic manipulation and may require the use of numerical methods to find the exact solution.