
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 12th, 2017, 11:16 AM  #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 11:19 AM. 
October 12th, 2017, 12:07 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,327 Thanks: 2451 Math Focus: Mainly analysis and algebra 
By simplifying the expressions.

October 12th, 2017, 12:34 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, 05:49 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,327 Thanks: 2451 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).


Tags 
analisys, inequality, real 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Triangle Inequality: Prove Absolute Value Inequality  StillAlive  Calculus  5  September 2nd, 2016 11:45 PM 
what this mean in real?  MMath  Trigonometry  7  June 6th, 2016 12:33 AM 
real number x for which inequality  jemes  Algebra  4  November 26th, 2014 02:58 PM 
real mapping, functional inequality  mrjones  Real Analysis  2  January 26th, 2010 01:16 PM 
Real numbers inequality (01/01/07)  julien  Math Events  0  April 30th, 2007 12:22 AM 