Step 1:
Using the property of logarithms that $b \log a = \log a^b$, we can rewrite each term as follows:
$$
2 \log \left(x^{2}-1\right) = \log \left(x^{2}-1\right)^{2}
$$
$$
4 \log (x-2) = \log (x-2)^{4}
$$
$$
\frac{1}{2} \log y = \log y^{\frac{1}{2}}
$$
So the
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