Question

Log3 (x²-16)>2 решить логарифмической неравенство ​

Answer 1

Решение на фото

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Answer 2

To solve the logarithmic inequality log₃(x² - 16) > 2, we can use the properties of logarithms to rewrite it in exponential form and solve for x.

First, recall that logₐ(b) > c is equivalent to a^c < b.

Using this property, we can rewrite the inequality as: 3² > x² - 16

Simplifying, we have: 9 > x² - 16

Next, let's isolate the x² term by adding 16 to both sides: 9 + 16 > x² 25 > x²

To solve for x, we can take the square root of both sides, considering both the positive and negative square roots: √25 > √x² ±5 > x

Therefore, the solution to the logarithmic inequality log₃(x² - 16) > 2 is x < -5 or x > 5.