Find all solutions of the equation ln(x) - ln(x-4)=8?

Question

I collapsed the natural log into one and then exponentiated to get e^8 = x/x-4 and then I cross-muliplied and solved for x to get 4e^8/1-e^8. For some reason that's not right. Anyone know the correct answer and how to get there? Thanks a ton.

Answer 1

ln(x) - ln(x-4)=8
ln (x/(x-4))=8
x/(x-4)=e^8
x=e^8(x-4)
x(1-e^8)=-4e^8
x= 4e^8/(e^8-1)

i believe that in your answer you forgot to multipy the 4 by -1.

Answer 2

ln(x) - ln(x - 4) = 8
ln(x/(x - 4)) = 8
x/(x - 4) = e^8
x = xe^8 - 4e^8
-xe^8 + x = -4e^8
-x(e^8 - 1) = -4e^8
x(e^8 - 1) = 4e^8
x = (4e^8)/(e^8 - 1)

Here is why your answer isn't right

(4e^8)/(1 - e^8) = (4e^8)/(-e^8 + 1) = (4e^8)/(-(e^8 - 1)) = (-4e^8)/(e^8 - 1)

as you can see, one is negative and the other is positive.

Answer 3

ln(x) - ln(x-4) = 8
ln(x/(x-4)) = 8
x/(x-4) = e^8
x = x*e^8 - 4e^8
x(e^8-1) = 4e^8
x = 4e^8/(e^8-1)

Seems to me you dropped the sign on -4e^8

Answer 4

rearange to:
Ln(x/(x-4))=8
take exp:
x/(x-4)=e^8
x=(x-4)*e^8
x=4*e^8/(e^8-1)=1.3866

Answer 5

blah!