How do you solve $lnx=3+ln(x-5)$ ?

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Answer 1 · 2016-03-09T13:10:27

$x=5/(1-e^-3)$

Transposing term in $lnx=3+ln(x-5)$

$lnx-ln(x-5)=3$ or

$ln(x/(x-5))=3$ - as $lna-lnb=ln(a/b)$

Hence, as $lna=brArra=e^b$

$(x/(x-5))=e^3$ or

$x=(x-5)e^3$ or

$(e^3-1)x=5e^3$ or

$x=(5e^3)/(e^3-1)$ or $x=5/(1-e^-3)$

How do you solve lnx=3+ln(x-5)lnx=3+ln(x-5)?