# ln (x+3)-ln (x-1) = ln 5

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### 2 Answers

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` ln(a/b) = ln a - ln b`

Thus, `ln (x+3) - ln (x-1) = ln 5` can be written as

`ln ( (x+3)/(x-1) ) = ln 5 `

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Therefore we get

`(x+3)/(x-1) = 5`

x+3 = 5x - 5

5 +3 = 5x -x

8 = 4 x

x = 2

note that lna - lnb = ln(a/b) !!

Using this formula, the given equation ln(x+3) - ln(x-1) can be expressed in the other way, ln(x+3/x-1).

ln(x+3/x-1) = ln5

Therefore, (x+3)/(x-1) = 5

x+3 = 5x-5

=> 4x = 8

=> x = 2

Therefore, x = 2