Log_100(25-2x)-log_100(75-7x) = 3-81^log_81(3)

Предыдущий
вопрос Следующий
вопрос

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.