SOLUTION: log3 (x+2) + log3(x-2) = 1

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Question 113581: log3 (x+2) + log3(x-2) = 1
Answer by solver91311(12135) About Me  (Show Source):
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log%283%2C%28x%2B2%29%29%2Blog%283%2C%28x-2%29%29=1

The sum of the logs is equal to the log of the product, so:

log%283%2C%28x%2B2%29%28x-2%29%29=1

Now, since log%28b%2Cx%29=y is equivalent to x=b%5Ey, we can write:

%28x%2B2%29%28x-2%29=3%5E1

Applying FOIL we get:

x%5E2-4=3
x%5E2-7=0
x=sqrt%287%29 or x=-sqrt%287%29