How do you solve for x in $ln(x+2) - ln(x-2) = ln3$ ?

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Answer 1 · 2016-04-16T08:52:04

$x = 4$

One $log$ minus another $log$ can be condensed as the inside of the first divided by the inside of the second, all inside a single $log$ , so

$ln(x+2) - ln(x-2) = ln((x+2)/(x-2))$

which gives us

$ln((x+2)/(x-2)) = ln3$ .

Raising both sides by $e$ and using simple algebraic manipulation, we can solve for $x$ ,

$(x+2)/(x-2) = 3$

$x+2 = 3(x-2)$
$x+2 = 3x - 6$
$8 = 2x$
$4 = x$

How do you solve for x in ln(x+2) - ln(x-2) = ln3 ln(x+2) - ln(x-2) = ln3?