SOLUTION: hi i am having a little trouble with this one Lnx+Ln(x+12)=1. I kind of remember that due to the fact that it is an addition problem you use multiplication but i dont remember ho

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: hi i am having a little trouble with this one Lnx+Ln(x+12)=1. I kind of remember that due to the fact that it is an addition problem you use multiplication but i dont remember ho      Log On


   

Question 237827: hi i am having a little trouble with this one Lnx+Ln(x+12)=1. I kind of remember that due to the fact that it is an addition problem you use multiplication but i dont remember how!
Paul
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the logs is the log of the product.



So



But we also know that:



So





and





John

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Lnx+Ln(x+12)=1.
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ln(x(x+12)) = 1
x(x+12) = e^1
x^2 + 12x - e = 0
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x = [-12 +- sqrt(144 - 4*1*-e)]/2
---
x = [-12 +- sqrt(154.87)]/2
----
x = [-12 +- 12.44)]/2
----
Only the positive solution satisfies the original equation:
x = [-12 + 12.44]/2
---
x = 0.44/2 = 0.22
-------------------
Cheers,
Stan H.