Question 533803
<pre>
                   {{{3^(x+2)}}} = {{{6^(2x)}}}

Take log base 12 of both sides:

              {{{log(12,(3^(x+2)))}}} = {{{log(12,(6^(2x)))}}}

              {{{(x+2)log(12,(3))}}} = {{{2x*log(12,(6))}}}

              {{{(x+2)log(12,(3))}}} = {{{2x*log(12,(6))}}}

              {{{(x+2)log(12,(3))}}} = {{{2x*log(12,(3*2))}}}

              {{{(x+2)log(12,(3))}}} = {{{2x(log(12,(3))+log(12,(2)))}}}

To make things easier, let {{{log(12,(3))}}} = A and let {{{log(12,(2))}}} = B

              (x + 2)*A = 2x(A + B)
                Ax + 2A = 2Ax + 2Bx 
                     2A = Ax + 2Bx
                     2A = x(A + 2B)
                  {{{(2A)/(A+2B)}}} = x
Therefore:

x = {{{(2A)/(A+2B)}}} = {{{(2log(12,(3)))/(log(12,(3))+2log(12,(2)))}}} = {{{(log(12,(3^2)))/(log(12,(3))+log(12,(2^2)))}}} = {{{(log(12,(9)))/(log(12,(3))+log(12,(4)))}}} = {{{(log(12,(9)))/(log(12,(3*4)))}}} = {{{(log(12,(9)))/(log(12,(12)))}}} = {{{(log(12,(9)))/1}}} = {{{log(12,(9))}}}
               
Edwin</pre>