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\frac{\log_{e}\left(|u+1|\right)+\log_{e}\left(|u-1|\right)}{4}
Factor out \frac{1}{4}.
\frac{\ln(|u+1|)+\ln(|u-1|)}{\ln(e)}
Consider \ln(|u+1|)\times \frac{1}{\ln(e)}+\ln(|u-1|)\times \frac{1}{\ln(e)}. Factor out \frac{1}{\ln(e)}.
\frac{\ln(|u+1|)+\ln(|u-1|)}{4\ln(e)}
Rewrite the complete factored expression.