How do you solve ln(2x+1) = 2 - ln(x)? Precalculus Solving Exponential and Logarithmic Equations Logarithmic Models 1 Answer RedRobin9688 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 Answer link Related questions What is a logarithmic model? How do I use a logarithmic model to solve applications? What is the advantage of a logarithmic model? How does the Richter scale measure magnitude? What is the range of the Richter scale? How do you solve 9^(x-4)=81? How do you solve logx+log(x+15)=2? How do you solve the equation 2 log4(x + 7)-log4(16) = 2? How do you solve 2 log x^4 = 16? How do you solve 2+log_3(2x+5)-log_3x=4? See all questions in Logarithmic Models Impact of this question 10820 views around the world You can reuse this answer Creative Commons License