
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 7th, 2016, 12:23 AM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  exponential inequality
Consider the inequality $9^xa\cdot 3^xa+3\leq 0,$ where $a$ is a real parameter. Find the value of $a$ so that $(1)$ The inequality has at least one negative solution $(2)$ The inequality has at least one positive solution Last edited by skipjack; November 7th, 2016 at 12:52 AM. 
November 7th, 2016, 09:23 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,404 Thanks: 1306 
write $u=3^x$ and solve the resulting quadratic. $3^x$ is monotonic increasing in $x$ so you can then solve for $x$ from $u$ and the inequalities remain unchanged. 

Tags 
exponential, inequality 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
exponential inequality  panky  Algebra  3  November 8th, 2016 03:22 AM 
exponential inequality  panky  Algebra  2  June 4th, 2016 03:25 AM 
solve exponential inequality  mared  Algebra  4  September 5th, 2014 03:13 PM 
Exponential function inequality  Fate  Algebra  2  April 29th, 2014 04:58 PM 
Exponential inequality  sphinn  Algebra  1  September 23rd, 2010 11:46 PM 