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

1 Answer
Jun 27, 2018

ln(2x+1)=2-ln(x)

e^(ln(2x+1))=e^(2-ln(x))

2x+1=e^2/x

2x^2+x=e^2

2x^2+x-e^2=0

x=(-1+-sqrt((1+8(e^2))))/4

2*(-1-sqrt((1+8(e^2))))/4+1<0

Therefore ln(2*(-1-sqrt((1+8(e^2))))/4+1) is not defined and not a valid input for x.

This means x=(-1+sqrt((1+8(e^2))))/4