Question 455264
<pre>
Solve the equation for x: 2log base 5 of x + log base 5 of 3 = log base 5(1/125)

The other person's answer, {{{x = sqrt(15/75)}}} is WRONG!!

{{{2*log (5, (x)) + log (5, (3)) = log (5, (1/125))}}}, with x > 0
{{{log (5, (x^2)) + log (5, (3)) = log (5, (1/125))}}}
       {{{log (5, (3x^2)) = log (5, (1/125))}}}
             {{{3x^2 = 1/125}}}
              {{{x^2 = (1/125)/3}}}
              {{{x^2 = (1/125) * (1/3)}}}
              {{{x^2 = 1/375}}}
             {{{highlight_green(highlight(highlight_green(x = sqrt(1/375))))}}}       OR      {{{x = -sqrt(1/375)}}} <==== IGNORE


             {{{highlight_green(highlight(highlight_green(x = sqrt(1/375))))}}} is an ACCEPTED solution, while {{{highlight(x = -sqrt(1/375))}}} is NOT, because the LATTER is NOT > 0,
                         but the FORMER is (see constraint above).</pre>