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

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Answer 1 · 2016-09-23T15:02:52

$x=4$ , is the Soln.

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

Since, $lna-lnb=ln(a/b)$ , we have,

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

We know that, $ln$ is $1-1$ function, so, we get,

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

By Compodando-Dividando,

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

$:. (2x)/4=x/2=4/2=2$

$:. x=4$

We see that this root satisfy the given eqn.hence,

$x=4$ , is the Soln.

How do you solve ln(x+2) - ln(x-2) = ln3ln(x+2) - ln(x-2) = ln3?