Question 71721
<pre>
log base 2 x ^(log base 2 x) =4

The other person only had 1 of the 2 solutions. Plus, the calculator was
used to get that answer. I don't think that that's what's expected!

{{{log (2, (x^(log (2, (x))))) = 4}}}
       {{{x^(log (2, (x))) = 2^4}}} --------- Converting to EXPONENTIAL form
       {{{x^(log (2, (x))) = 16}}}
          {{{log (2, (x)) = log (x, (16))}}} ---- Converting to LOGARITHMIC form
          {{{log (2, (x)) = log ((16))/log ((x))}}}
          {{{log (2, (x)) = log (2, (16))/log (2, (x))}}} ---- Converting right-side to base 2
          {{{log (2, (x)) = 4/log (2, (x))}}}
      {{{(log (2, (x)))^2 = 4}}} ------- Cross-multiplying
  {{{sqrt((log (2, (x)))^2) = 0+-sqrt(4)}}} ---- Taking sqrt of both sides
         {{{log (2, (x)) = 0 +- 2}}}
         {{{log (2, (x)) = 2}}}            OR    {{{log (2, (x)) = - 2}}}
            {{{highlight(highlight_green(highlight(x))) = 2^2 = highlight(highlight_green(highlight(4)))}}}     OR     {{{highlight(highlight_green(highlight(x))) = 2^(- 2) = highlight(highlight_green(highlight(1/4)))}}}</pre>