Question 1082504
<pre>
Hi!! What is log base 4 of X - log base 16 of (x+3) = 1/2

 {{{log (4, (x)) - log (16, (x + 3)) = 1/2}}}
{{{2*log (2, (x)) - log (2, (x + 3)) = 2}}} ----- Converting from base 4 and base 16 to base 2 
{{{log (2, (x^2)) - log (2, (x + 3)) = 2}}} ----- Applying {{{a*log (b, (c)) = log (b, (c^a))}}}
       {{{ log (highlight(2), (x^2/(x + 3))) = highlight_green(2)}}} ---- Applying {{{log (a, (b)) - log (a, (c)) = log (a, (b/c))}}} 
              {{{x^2/(x + 3) = highlight(2)^highlight_green(2)}}} --- Converting to EXPONENTIAL form
              {{{x^2/(x + 3) = 4}}}
                 {{{x^2 = 4(x + 3)}}} ----- Cross-multiplying
                 {{{x^2 = 4x + 12}}}
         {{{x^2 - 4x - 12 = 0}}}
     (x - 6)(x + 2) = 0 ----- Factoring trinomial
x - 6 = 0      OR      (x + 2) = 0 ---- Equating each factor to 0
   <font color = red><font size = 4><b>x = 6</font></font></b>      OR       x = - 2 (IGNORE, as this is an EXTRANEOUS solution!

So, only ONE (1) solution applies here, so accept NO OTHER.</pre>