Answer
$x=4$
Work Step by Step
$log(x+1)+log(x-2)=1$,
$log[(x+1)(x-2)]=1$,
$log(x^2-x-2)=1$,
$x^2-x-2=10^1$,
$x^2-x-12=0$,
$(x+3)(x-4)=0$,
$x=-3, 4$, check, only $x=4$ fits.
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