How do you solve $Ln (x) - Ln (x-1) = Ln (3)$ ?

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Answer 1 · 2015-12-30T05:55:44

$x=3/2$

$ln(x)-ln(x-1)=ln3$
We know that:

$ln(y/z)=lny-lnz$

Here $y=x and z=x-1$
$implies ln(x/(x-1))=ln3$

$implies (x/(x-1))=3$

$implies x=3(x-1)$
$implies x=3x-3$
$implies 2x=3$
$implies x=3/2$

How do you solve Ln (x) - Ln (x-1) = Ln (3)Ln (x) - Ln (x-1) = Ln (3)?