$$\frac{1}{3}\log_{a}(x-1)^{3}+\frac{10}{9}\log_{a}(x+1)-\frac{1}{9}\log_{a}(x+1)$$
$\frac{\ln(x+1)+\ln(x-1)}{\ln(a)}$
$$\frac{3\log_{a}\left(\left(x-1\right)^{3}\right)+10\log_{a}\left(x+1\right)-\log_{a}\left(x+1\right)}{9}$$
$$\frac{3\ln(\left(x-1\right)^{3})+10\ln(x+1)-\ln(x+1)}{\ln(a)}$$
$$\frac{3\ln(\left(x-1\right)^{3})+10\ln(x+1)-\ln(x+1)}{9\ln(a)}$$
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