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

Question

1835 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-09T15:22:26

#color(blue)(x=(-e^2)/(1-e^2)~~1.156517643)#

#lna-lnb=ln(a/b)#

#lnx-ln(x-1)=2#

#ln(x/(x-1))=2#

#e^(ln(x/(x-1)))=e^2#

#x/(x-1)=e^2#

#x-e^2x=-e^2#

#x(1-e^2)=-e^2#

#x=(-e^2)/(1-e^2)~~1.156517643#