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October 12th, 2017, 11:16 AM   #1
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Inequality in real Analisys

Find all the solutions of $$\sqrt{(log_9 |x| -1)log_3(x^2)}>(1/2) - 2log_9 |x|$$

How can I start?

Last edited by Berker; October 12th, 2017 at 11:19 AM.
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October 12th, 2017, 12:07 PM   #2
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By simplifying the expressions.
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October 12th, 2017, 12:34 PM   #3
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Maybe I get $$\sqrt{log_9 x \cdot 2 \frac{log_9 x}{log_9 3} -2 \frac{log_9 x}{log_9 3}}>(1/2) -2log_9 x$$
But I have some problems with the different cases of |x|>0.
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October 12th, 2017, 05:49 PM   #4
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I'm sure you can replace $\log_9 3$ with a number. You could also turn the right hand side into a single logarithmic term (by replacing $\frac12$ with a suitable logarithmic expression), which makes it easier to square the equation (being careful with the direction of the inequality in the two cases).
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