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

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Answer 1 · 2018-07-09T15:22:26

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

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

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

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

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

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

$x-e^2x=-e^2$

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

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

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