# How do you solve the equation log(3+x)-log(x-5)=log(2)?

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John D.
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Feb 9, 2018

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Use the logarithm property that:

#loga - logb = log(a/b)#

Therefore, we can solve this equation like this:

#log(3+x) - log(x-5) = log(2)#

#log((3+x)/(x-5)) = log(2)#

#(3+x)/(x-5) = 2#

#3+x = 2(x-5)#

#3+x = 2x - 10#

#3 = x - 10#

#13 = x#

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