Answer
a. $x=-1$, $x=3$
b. $x=\frac{1}{3}$
Work Step by Step
a.
$\log_{3}x+\log_{3}(x-2)=1$
$\log_{3}(x(x-2))=1$
$3^1=x^2-2x$
$3=x^2-2x$
$0=x^2-2x-3$
$0=(x+1)(x-3)$
$x=-1$, $x=3$
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b.
$\log_{10}(x+3)-log_{10}x=1$
$\log_{10}(\frac{x+3}{x})=1$
$10^1=\frac{x+3}{x}$
$10x=x+3$
$9x=3$
$x=\frac{1}{3}$
