Question 1207490
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<pre>

    {{{(5^(log((x))-1))/125}}} =  {{{(1/5)^(log((x))^2-log((x)))}}}


Write right part with the base 5


    {{{(5^(log((x))-1))/125}}} =  {{{5^(log((x))-log((x))^2)}}}


Simplify left side

    {{{5^(log((x))-4)}}} = {{{5^(log((x))-log((x))^2)}}}.


Since the bases are equal, it implies that the indexes are equal, too

    log(x)-4 = log(x) - (log(x))^2


Simplify

     -4 = -(log(x))^2

      4 = (log(x))^2


Take square root of both sides

      log(x) = +/- {{{sqrt(4)}}}

      log(x) = +/- 2


There are two solutions:  x= {{{10^2}}} = 100  and  x= {{{10^(-2)}}} = 0.01.    <U>ANSWER</U>
</pre>

Solved.