SOLUTION: Solve the equation log(x+2)+log(x-2)=log5

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Question 1176006: Solve the equation log(x+2)+log(x-2)=log5
Found 3 solutions by MathLover1, ewatrrr, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%28x%2B2%29%2Blog%28x-2%29=log%285%29
log%28%28x%2B2%29%28x-2%29%29=log%285%29
%28x%2B2%29%28x-2%29=5
x%5E2+-+4=5
x%5E2+=5%2B4
x%5E2+=9
x+=sqrt%289%29
solutions:
x+=3 or
x+=-3-> since log, disregard negative solution
so, your solution is: x+=3


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi

log(x+2)+log(x-2)-log5 =0 

Log((x+2)(x-2)/5)= 0
(x+2)(x-2)/5) = 10^0 = 1
(x+2)(x-2) = 5
 x^2 - 4 = 5
  x^2 = 9
   x = ±3  Tossing out negative solution for a Logarithm
   x = 3

Log 1 = 0  checks
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Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

Looking into the post by @ewatrrr, too confiding reader may think that both roots x = 3 and x= -3 are the solution.


There is nothing more far from the true than that.


x= 3 is the solution, while x= -3  IS NOT:  logarithm does not allow negative arguments.


ANSWER.  The only solution is  x= 3.