Question

Ln (x+1) - Ln (x-1) = 3

Answer 1

Use log properties and combine

ln[(x+1)/(x-1)] = 3

raise both sides by e

(x+1) / (x-1) = e^3

x+1 = e^3(x-1)

x+1 = xe^3 - e^3

x-xe^3 = -e^3 - 1

x(1-e^3) = -e^3-1

x = (-e^3-1) / (1-e^3)

Have a good day!

Answer 2

note that lna-lnb = ln(a/b) and lne^x=x
ln(x+1)-ln(x-1)=3
ln((x+1)/(x-1))=lne^3
((x+1)/(x-1))= e^3
((x+1)/(x-1))(x-1) = e^3 (x-1)
x+1 = (x-1)e^3
= xe^3 -e^3
x+1-xe^3=xe^3-e^3 -xe^3
x-xe^3+1-1=-e^3 -1
(1-e^3)x=-e^3-1
x=(-e^3-1)/(1-e^3)

Answer 3

Sorry that I am a bit slow

Answer 4

so what is equal continued

x= -(e^3 +1)/(-(e^3 -1) = (e^3 +1)/(e^3 -1)

Answer 5

hope you like it !!!

Answer 6

yes i know but this is the final result

Answer 7

oh wait...thought expanding to cubey thingy makes difference..seems not