Question 481624
<pre>
Solve:

2 * log--base4 (x) + 3 * log--base8 (x)=10
******************************************<font color = blue><font size = 2><font face = tahoma><b>
Respondent @wsshak3(11628) came up with a decimal value for x, but this problem clearly has an INTEGER-solution, as
seen below!! While both are close to each other, the approximated decimal-answer doesn't QUITE MAKE the equation true,
but ALMOST TRUE, while the INTEGER-value for x, below, does.

                   {{{2log(4, (x)) + 3log (8, (x)) = 10}}}
    {{{2(log ((x))/log ((4))) + 3(log ((x))/log ((8))) = 10}}}
{{{2(log (2, (x))/log (2, (4))) + 3(log (2, (x))/log (2, (8))) = 10}}} ---- Converting ALL logs to base 2
       {{{2(log (2, (x)))/2 + 3(log (2, (x)))/3 = 10}}}
   {{{cross(2)(log (2, (x)))/cross(2) + cross(3)(log (2, (x)))/cross(3) = 10}}}
                      {{{log(2, (x)) + log (2, (x)) = 10}}}
                                    {{{2log(2, (x)) = 10}}} 
                                      {{{log (2, (x)) = 10/2}}}
                                      {{{log (2, (x)) = 5}}}
                                                 {{{x = 2^5}}} ----- Converting to EXPONENTIAL form
                                               {{{highlight(x) = highlight(32))}}}</font></font></font></b></pre>