How do you solve #ln(x+1)-ln(x-2) = ln x#?

1 Answer
Lucy
Apr 3, 2018

#x=3.30#

Explanation:

#In(x+1)-In(x-2)=Inx#
#In(x+1)/(x-2)=Inx#
#(x+1)/(x-2)=x#
#x+1=x(x-2)#
#x+1=x^2-2x#
#x^2-3x-1=0#

Using quadratic formula,
#x=(3+-sqrt(9+4))/2#
#x=(3+sqrt13)/2 or (3-sqrt13)/2#
#x=3.30 or -0.302#

BUT you can't log a NEGATIVE number so #x=-0.302#

Therefore, #x=3.30# is the only answer

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