SOLUTION: Ln(x-1)+Ln(x+3)=Ln5 Cannot figure out how to solve, please help

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Question 201009: Ln(x-1)+Ln(x+3)=Ln5
Cannot figure out how to solve, please help
Found 2 solutions by solver91311, RAY100:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Given the same base, the sum of the logs is the log of the product, and if two logs to the same base are equal, then their arguments must be equal.

Symbolically,



and



So:



and therefore



so



Solve the quadratic by ordinary methods -- this one will factor neatly.

John

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x-1) + ln (x+3) = ln 5
.
remember lna+lnb =ln(ab)
.
ln{(x-1)(x+3)} = ln5
.
(x-1)(x+3) =5
.
x^2 +2x -3 =5
.
x^2 +2x -8 =0
.
(x+4)(x-2) = 0
.
x = -4, x=2
.
check
.
(x=2),,,,ln { (2)-1} +ln{(2) +3} = ln5,,,,ln 1 +ln 5 =ln5,,,,,ok
.
(x=-4),,ln{ (-4)-1} +ln{(-4)+3} =ln5,,ln-5 +ln-1 =ln5,,,ln(-5*-1) =ln5,,,ok