\Lambda(n)=\sum_{d|n} \mu(d)\log\left(\frac{n}{d}\right)=\sum_{d|n} \mu(d)(\log n-\log d)=-\displaystyle\sum_{d|n}\mu\left(d\right)\log{d}+\log n\sum_{d|n}\mu(d)=-\displaystyle\sum_{d|n}\mu\left(d\right)\log{d}