SOLUTION: I have to solve the equation, using properties of logarithms. ln x- ln(x-1)= 2 Thank you so much if you can help me.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I have to solve the equation, using properties of logarithms. ln x- ln(x-1)= 2 Thank you so much if you can help me.       Log On


   

Question 444436: I have to solve the equation, using properties of logarithms.
ln x- ln(x-1)= 2
Thank you so much if you can help me.
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

ln x- ln(x-1)= 2

ln (x/(x-1) = 2

  e^2 = x/(x-1)

 7.389 = x/(x-1)

 7.389(x-1) = x

  6.389x = 7.389

       x = 1.1565

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




The difference of the logs is the log of the quotient:



Use the definition of logarithms:



to write:



And then do the algebra to obtain:



Use your calculator if you need a numeric approximation.

John

My calculator said it, I believe it, that settles it
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