Question 1209836
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Find x if log_2 x^2 + log_{1/2} x + 3*log_4 x = 5.
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<pre>
      <U>Step by step</U>


The domain to this equation is the set of all real positive numbers,
so we work in this domain.


    {{{log(2,x^2)}}} = {{{2*log(2,x))}}}.


    {{{log(1/2,x)}}} = {{{-log(2,x)}}}.


    {{{3*log(4,x)}}} = {{{(3/2)*log(2,x)}}}.


Therefore, the whole given equation is equivalent to this one

    {{{2*log(2,x))}}} - {{{log(2,x)}}} + {{{(3/2)*log(2,x)}}} = 5.


Simplify

    {{{(5/2)*log(2,x)}}} = 5,

    {{{log(2,x)}}} = {{{5/((5/2))}}} = 2

     x = {{{2^2}}} = 4.


<U>ANSWER</U>.  x = 4.
</pre>

Solved.