SOLUTION: Solve for x algebraically: {{{log(2,x)+log(2,x+2)-log(2,4-x)=2}}}

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Question 258141: Solve for x algebraically: log%282%2Cx%29%2Blog%282%2Cx%2B2%29-log%282%2C4-x%29=2
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Remember when you add logs this is the same a multiplying big information. When you subtract logs this is the same as dividing big information. Using rules of logs we get
(i) log%282%2Cx%28x%2B2%29%2F%284-x%29%29=2
now, rewriting using exponents, we get
(ii) 2%5E2+=+x%28x%2B2%29%2F%284-x%29
cross multiply to get
(ii) 4%284-x%29+=+x%5E2+%2B+2x
setting = 0, we get
(iv) x%5E2+%2B+2x+%2B+4x+-+16+=+0
simplify to get
(v) x%5E2+%2B+6x+-+16+=+0
factor to get
(vi) %28x%2B8%29%28x-2%29+=+0
solving for x, we get
x = -8
or
x = 2.
Since x = -8 is not a solution, we are left with x = 2.