Question

How to solve:
In(x+3) - In(x-1) = 3

Answer 1

x = (e^3 +3)/(e^3 -1) ≈ 1.20958

Explanation:

Take the antilog and solve in the usual way.

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

ln((x +3)/(x -1)) = 3 . . . . rearrange to a single log

(x +3)/(x -1) = e^3 . . . . take the antilog

x +3 = e^3·(x -1)

3 +e^3 = x(e^3 -1)

x = (e^3 +3)/(e^3 -1) ≈ 1.20958

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Check

This answer checks OK in the original equation:

ln(4.20958) -ln(0.20958) = 3