SOLUTION: Solve for x log(base 25)(x+1) + log(base 25)(x-3) = 1/2

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Question 1208397: Solve for x
log(base 25)(x+1) + log(base 25)(x-3) = 1/2
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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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 

    log%2825%2C%28x%2B1%29%29 + log%2825%2C%28x-3%29%29 = 1%2F2

    log%2825%2C%28%28x%2B1%29%2A%28x-3%29%29%29 = 1%2F2


Use the fact that  log%2825%2C5%29 = 1%2F2  and replace  1%2F2  in the right side 
of the previous equation by  log%2825%2C5%29 = 1%2F2.  You will get

    log%2825%2C%28%28x%2B1%29%2A%28x-3%29%29%29 = log%2825%2C5%29.


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%289%29 = +/- 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.


ANSWER.  The only solution is x= 4.

Solved.