Question

solve : ln x = 1 + ln (x+1)

Answer 1

@camilasanchez where exactly are you stuck in this question?

Answer 2

ln x = 1 + ln (x+1)

ln|x| -1 - ln|x + 1| = 0

combine the logs
ln | (x) / (x +1) | -1 = 0

ln | (x) / (x +1) | = 1

(x) / (x + 1) = e

x = e(x + 1)
x = ex + e
(1 - e)x = e
x = (e) / (1 -e)

Answer 3

ln(x)-ln(x+1)=1
ln(x/x+1)=ln(e)
(x)/(x+1)=e
x=(x+1)e
x=xe+e
x(1-e)=e
x=(e)/(e-1)

Answer 4

@nitz Check your penultimate step and the last step, please. I didn't follow how
the (1-e) became (e-1). Thanks.

Answer 5

sorry.....its
x=xe+e
x-xe=e
x(1-e)=e
x=e/(1-e)

Answer 6

just a reminder...
don't post direct entire solutions, its against CoC.

Answer 7

thanks !

Answer 8

sorry @hartnn