Logx+1(x^2-3x+11)=-1

Предыдущий
вопрос Следующий
вопрос

To solve the given equation, we will first simplify the left side by using the properties of logarithms.

Using the property log_b(A) + log_b(B) = log_b(A * B), we can rewrite the equation as follows:

logx(x^2 - 3x + 11) = logx(1/x)

Now, we can remove the logarithms by converting both sides to their exponential form:

x(x^2 - 3x + 11) = 1/x

Multiplying both sides by x to clear the fraction:

x^3 - 3x^2 + 11x = 1

Now, we have a cubic equation that we can solve by setting it equal to 0:

x^3 - 3x^2 + 11x - 1 = 0

This equation does not factor easily, so we can use numerical methods such as the cubic formula or approximation techniques.

Using numerical methods, we can find the approximate solution to be:

x ≈ 0.8004

So, the solution to the equation is approximately x = 0.8004.