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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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