How do you solve #log _ 5 (x-3)+log _ 5(x+1) = log _ 5(x+3)#?

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Answer 1 · 2015-12-13T22:19:19

#x=(3+sqrt33)/2#

Combine using logarithm rules.

#log_5((x-3)(x+1))=log_5(x+3)#

Raise both sides to the #5#th power.

#5^(log_5((x-3)(x+1)))=5^(log_5(x+3))#

#(x-3)(x+1)=x+3#

#x^2-2x-3=x+3#

#x^2-3x-6=0#

#x=(3+-sqrt(9+24))/2=(3+-sqrt33)/2#

Throw out the negative answer. It cannot be used because a logarithm has to be a function of a POSITIVE number.

Thus, #x=(3+sqrt33)/2#.