SOLUTION: What is the solution set of the inequality {{{log(1/3,x^2+3x+4) <= -1}}}?

Let the left side = y





Take the log base 10 of both sides







The original inequality was



So .  Substituting for y



We know that  is a negative 
number, so when we multiply both sides
of the inequality by it, the inequality
symbol will reverse:



Use a principle of logarithms to rewrite
the right side:



Since raising to the -1 power is the same
as taking the rciprocal, the above becomes:



Since logs base 10 are in ascending order,





That has critical numbers

 

 

Put those two values on a number line and
choose a test point in each region to discover that
the solution set is

  or 

Edwin