Two log series coincide

Let $$S=\sum_{k=1}^{\infty}(-1)^{k-1}\frac{1}{k}\left(\frac{1}{4}\right)^{k}\quad\text{and}\quad T=\sum_{k=1}^{\infty}\frac{1}{k}\left(\frac{1}{5}\right)^{k}.$$ Then, which of the following statements is TRUE?