How do you solve $2ln(x+3) + ln(x-2) - (1/2)ln(x-2) = ln(x-2) - lnsqrt( x-2)$ ?

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Answer 1 · 2016-07-03T10:22:27

$x=-2$

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

$=>2ln(x+3)+cancel(ln(x-2))-cancel(lnsqrt(x-2))-cancel(ln(x-2))+cancel(lnsqrt(x-2))=0$

$=>ln(x+3)=0$

$=>x+3=e^0=1$

$:.x=1-3=-2$

How do you solve 2ln(x+3) + ln(x-2) - (1/2)ln(x-2) = ln(x-2) - lnsqrt( x-2)2ln(x+3) + ln(x-2) - (1/2)ln(x-2) = ln(x-2) - lnsqrt( x-2)?