SOLUTION: log(x+2)to base 3+log(10-x)to base 3-3=0

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Question 619407: log(x+2)to base 3+log(10-x)to base 3-3=0
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
log(x+2)to base 3+log(10-x)to base 3-3=0
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log3(x+2) + log3(10-x) = 3
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log3[(x+2)(10-x)] = 3
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(x+2)(10-x) = 3^3
-x^2+8x+20 = 27
x^2 -8x + 7 = 0
(x-7)(x-1) = 0
x = 7 or x = 1
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Cheers,
Stan H.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,



  3^3 = (x+2)(10-x) = 10x + 20 - x^2 - 2x

 27 = -x^2 + 8x + 20

   0 = -x^2 + 8x -7

   0 = x^2 - 8x + 7

      (x-7)(x-1) = 0 

        x = 7,1 

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