Rewrite the expression $4 \log x-2 \log \left(x^{2}+1\right)+2 \log (x-1)$ as a single logarithm \[ 4 \log x-2 \log \left(x^{2}+1\right)+2 \log (x-1)= \] Next Question

Step 1 ：The question is asking to rewrite the given expression as a single logarithm. To do this, we can use the properties of logarithms.

Step 2 ：The properties of logarithms that we will use are: 1. \(a \log b = \log b^a\) 2. \(\log a - \log b = \log \frac{a}{b}\) 3. \(\log a + \log b = \log ab\)

Step 3 ：Using these properties, we can rewrite the given expression as a single logarithm.

Step 4 ：The expression \(4 \log x-2 \log \left(x^{2}+1\right)+2 \log (x-1)\) can be rewritten as a single logarithm as follows:

Step 5 ：\(\boxed{\log \left(\frac{x^{4}(x-1)^{2}}{(x^{2}+1)^{2}}\right)}\)