Question 1208397
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Solve for x
log(base 25)(x+1) + log(base 25)(x-3) = 1/2
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                        Step by step


<pre>
    {{{log(25,(x+1))}}} + {{{log(25,(x-3))}}} = {{{1/2}}}

    {{{log(25,((x+1)*(x-3)))}}} = {{{1/2}}}


Use the fact that  {{{log(25,5)}}} = {{{1/2}}}  and replace  {{{1/2}}}  in the right side 
of the previous equation by  {{{log(25,5)}}} = {{{1/2}}}.  You will get

    {{{log(25,((x+1)*(x-3)))}}} = {{{log(25,5)}}}.


It implies

    (x+1)*(x-3) = 5

    x^2 + x - 3x - 3 = 5

    x^2 - 2x - 8 = 0

    (x^2 - 2x + 1) - 8 = 1

     x^2 - 2x + 1 = 1 + 8

      (x-1)^2 = 9

       x-1    = +/- {{{sqrt(9)}}} = +/- 3.


Hence, x is either -2 or 4.


Negative value x= -2 does not work in the original equation.


Hence,  x= 4  is the only solution.


<U>ANSWER</U>.  The only solution is x= 4.
</pre>

Solved.