SOLUTION: 1/2 loga (X+2)+ 1/2 loga(X-1)= 2/3 loga 27

Question 230394: 1/2 loga (X+2)+ 1/2 loga(X-1)= 2/3 loga 27

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1/2 loga (X+2)+ 1/2 loga(X-1)= 2/3 loga 27
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All these logs are loga
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log(x+2)^(1/2) + log(x-1)^(1/2) = log(27)^(2/3)
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log[(x+2)(x-1)]^(1/2) = log9
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[(x^2+x-2)^(1/2)] = 9
--------
Square both sides to get:
x^2+x-2 = 81
x^2+x-83 = 0
x = [-1 +- sqrt(1 -4*-83)]/2
x = [-1 +- sqrt(333)]/2
Positive solution:
x = 8.62..
===================
Cheers,
Stan H.
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