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 October 12th, 2017, 12:16 PM #1 Newbie   Joined: Oct 2017 From: Italy Posts: 15 Thanks: 0 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 12:19 PM.
 October 12th, 2017, 01:07 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,118 Thanks: 2369 Math Focus: Mainly analysis and algebra By simplifying the expressions.
 October 12th, 2017, 01:34 PM #3 Newbie   Joined: Oct 2017 From: Italy Posts: 15 Thanks: 0 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.
 October 12th, 2017, 06:49 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,118 Thanks: 2369 Math Focus: Mainly analysis and algebra 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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