Question

Решить уравнение log4(x^2-11x)=1-log1/4(2-x) Значения логарифмов написаны снизу справа

Answer 1

Решение в приложении.

Answer 2

Solving the Equation log4(x^2-11x) = 1 - log1/4(2-x)

To solve the equation log4(x^2-11x) = 1 - log1/4(2-x), we will follow these steps:

Step 1: Simplify the equation by using the properties of logarithms. Step 2: Solve for x.

Let's go through each step in detail.

Step 1: Simplify the Equation

Using the properties of logarithms, we can rewrite the equation as follows:

log4(x^2-11x) + log1/4(2-x) = 1

To combine the logarithms on the left side, we can use the property log a + log b = log (a * b). Applying this property, we get:

log4[(x^2-11x) * (2-x)] = 1

Now, we can rewrite the equation as an exponential equation:

4^1 = (x^2-11x) * (2-x)

Simplifying further, we have:

4 = (x^2-11x) * (2-x)

Step 2: Solve for x

To solve the equation 4 = (x^2-11x) * (2-x), we can expand the right side and set it equal to zero. Then, we can factor the resulting quadratic equation and solve for x.

Expanding the right side:

4 = (x^2-11x) * (2-x) 4 = 2x^3 - 13x^2 + 22x

Setting it equal to zero:

2x^3 - 13x^2 + 22x - 4 = 0

To solve this cubic equation, we can use numerical methods or approximation techniques. However, since the equation seems to have complex roots, it may not have simple solutions.

Unfortunately, I couldn't find any specific solutions for this equation in the available search results It is possible that the equation may require more advanced mathematical techniques to solve.

Please let me know if there's anything else I can help you with!