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tia_tia [17]
3 years ago
5

Ln (x-2) +ln (2x-3)=2ln x

Mathematics
1 answer:
goblinko [34]3 years ago
4 0
D:x-2\ \textgreater \ 0 \wedge 2x-3\ \textgreater \ 0 \wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2 \wedge x\ \textgreater \ \dfrac{3}{2}\wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2\\\\
\ln (x-2) +\ln (2x-3)=2\ln x \\
\ln (x-2)(2x-3)=\ln x^2\\
(x-2)(2x-3)=x^2\\
2x^2-3x-4x+6=x^2\\
x^2-7x+6=0\\
x^2-x-6x+6=0\\
x(x-1)-6(x-1)=0\\
(x-6)(x-1)=0\\
x=6 \vee x=1\\
1\not \in D\\
\boxed{x=6}
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