
X^2*log625 (x-6) <= log5 (x^2-12x+36)


Ответы на вопрос

Ответ:
Пошаговое объяснение:
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To solve the inequality , we need to follow a step-by-step process.
First, let's simplify the expressions using logarithmic properties:
Use the change of base formula to rewrite the logarithms: and .
Simplify the expressions further: (since ).
Now, the inequality becomes: .
Multiply both sides of the inequality by 4 to eliminate the fraction: .
Now, we have: .
Using the property : .
Divide both sides of the inequality by , noting that must be positive since the logarithm of a negative number is undefined: .
Take the square root of both sides (keeping in mind that we need to consider both the positive and negative square roots): or .
However, we need to make sure that the logarithms in the original expressions are well-defined. The logarithm must be positive, so . Additionally, in the expression , we need to make sure the argument inside the logarithm is positive, so , which simplifies to , which is always true for real except at .
So, considering all conditions together, the solution to the inequality is:


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