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

1 Answer
Dec 13, 2015

#x=(3+sqrt33)/2#

Explanation:

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#

Use the quadratic formula.

#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#.