How do you solve $Ln 12 - ln(x - 1) = ln(x-2)$ ?

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Answer 1 · 2016-08-28T10:43:05

$x=5$

$ln12-ln(x-1)=ln(x-2)$

$hArrln12/(x-1)=ln(x-2)$ or

$12/(x-1)=(x-2)$ or

$12=(x-1)(x-2)$ or

$x(x-2)-1(x-2)=12$ or

$x^2-2x-x+2=12$ or

$x^2-3x-10=0$ or

$x^2-5x+2x-10=0$ or

$x(x-5)+2(x-5)=0$ or

$(x-5)(x+2)=0$ or

$x=5$ or $x=-2$

But as $x=-2$ is extraneous as we cannot have log of a negative number,

Answer is $x=5$ .

How do you solve Ln 12 - ln(x - 1) = ln(x-2)Ln 12 - ln(x - 1) = ln(x-2)?