SOLUTION: solve for x: log 2 (x-1) - log 2 (x+2) + log2 (x+3) = 2

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Question 1206450: solve for x:
log 2 (x-1) - log 2 (x+2) + log2 (x+3) = 2


Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

The given equation is equivalent to

     = 

plus the condition that each factor in parentheses is positive number.


From it, we get

    (x-1)*(x+3) = 4*(x+2)

     x^2 - x + 3x - 3 = 4x + 8

     x^2 - 2x - 11 = 0


Apply the quadratic formula and find the roots

     =  =  =  = .


One root is x =  = 4.4641  (rounded).


Another root is   = -2.4641  (rounded).


Only positive root is the solution to the original equation, since (x-1) is also positive.


The negative root is not the solution to the original equation, since then (x-1) is negative, too.

Solved, with explanations.



Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
solve for :













...if log same, then













using quadratic formula we get






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