How do you solve #Ln x - Ln(x+1) = 1#?

1 Answer
Noah G
Dec 1, 2016

#O/#

Explanation:

Use the subtraction rule of logarithms that #log_a(n) - log_a(m) = log_a(n/m)#.

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

#x/(x + 1) = e^1#

#x = e(x + 1)#

#x = ex + e#

#x- ex = e#

#x(1 - e) = e#

#x= e/(1 - e)#

If you want an approximation, #x ~= -1.58#. However, since #x > 0# for the natural logarithms to be defined, this solution is extraneous.

Hopefully this helps!

Related questions
See all questions in Natural Logs
Impact of this question
3633 views around the world
You can reuse this answer
Creative Commons License