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

1 Answer
May 6, 2018

x = 1/(e^2 - 1)

Explanation:

ln(x+1)-lnx = 2

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

cancel(ln)((x+1)/x) = cancel(ln)(e^2)

(x+1)/x = e^2

x+1 = xe^2

1 = xe^2 - x

common factor

1 = x(e^2 - 1)

x = 1/(e^2 - 1)