Question 79779
<pre>
log(Base3)(x-1) -Log(base3)(x+2)=2

{{{log (3, (x - 1)) - log (3, (x + 2)) = 2}}}
For log (a), "a" MUST be > 0
So, we set the SMALLER "a" (x - 1) > 0____x > 1

We now get: {{{log (3, (x - 1)) - log (3, (x + 2)) = 2}}}, with <font color = red><font size = 5><b>x > 1</font></font></b>
{{{log (3, ((x - 1)/(x + 2))) = 2}}} --- Applying {{{log (a, (b)) - log (a, (c))}}} = {{{log (a, (b/c))}}}
      {{{(x - 1)/(x + 2) = 3^2}}} -- Converting to EXPONENTIAL form 
   9(x + 2) = x - 1 ---- Cross-multiplying
    9x + 18 = x - 1
     9x - x = - 1 - 18
         8x = - 19

As seen above, x is NEGATIVE (< 0), so x is NOT > 1. As a result, NO SOLUTIONS exist here!</pre>