This happens because negative values of x are a valid argument for ln(x^20) because the value inside ln() will remain positive anyway. However, for ln(x) negative values of x are invalid, hence the graph is plotted only on positive side of x-axis.

Its not too rare that common known formulas are a bit imprecise and don’t hold in all cases, more often than not this happens when absoulute values are involved.

\frac{20}{x} is the differentiation of both the \ln (x^{20}) and 20 \ln (x), I put it in the plot to show the difference of plots of \ln (x^{20}) and 20 \ln (x), even if the differentiation is the same