Question 921936
<pre>
log (base 7) 2 + log (base 49) x = log (base 1/7) sqrt 3
 {{{log (7, (2)) + log (49, (x)) = log (1/7, (sqrt(3)))}}}
   {{{log (7, (2)) + log ((x))/log ((49)) = log ((sqrt(3)))/log ((1/7))}}}
 {{{log (7, (2)) + log (7, (x))/log (7, (49)) = log (7, (sqrt(3)))/log (7, (1/7))}}} ---- Converting from base 10 to base 7
  {{{log (7, (2)) + log (7, (x))/2 = log (7, (sqrt(3)))/(- 1)}}}
  {{{log (7, (2)) + log (7, (x))/2 = (- log (7, (sqrt(3))))/1}}}
{{{2*log (7, (2)) + log (7, (x)) = - 2*log (7, (sqrt(3)))}}} ---- Multiplying by LCD, 2
 {{{log (7, (2)^2) + log (7, (x)) = log (7, (sqrt(3))^(- 2))}}} --- Applying {{{a*log (b, c)}}} = {{{log (b, (c)^a)}}}
  {{{log (7, (4)) + log (7, (x)) = log (7, (1/sqrt(3))^2)}}}
  {{{log (7, (4)) + log (7, (x)) = log (7, (1/3))}}}

         {{{log (7, (4x)) = log (7, (1/3))}}} ---- Applying {{{log (a, (b)) + log (a, (c)) = log (a, (b*c))}}}
               {{{4x = 1/3}}} ---- Applying b = c, WHEN {{{log (a, (b)) = log (a, (c))}}} 
              12x = 1 ------ Cross-multiplying
               {{{highlight(x = 1/12)}}}</pre>