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

-------------
All these logs are loga
-----------------------
log(x+2)^(1/2) + log(x-1)^(1/2) = log(27)^(2/3)
---
log[(x+2)(x-1)]^(1/2) = log9
---------------
[(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.