Logarithms' challenger #2

Algebra Level 2

\(\text{Find the value of:}\)\[\log_ {a}{\left(1-\frac{1}{2}\right)}+\log_ {a}{\left(1-\frac{1}{3}\right)}+\log_ {a}{\left(1-\frac{1}{4}\right)}...+\log_ {a}{\left(1-\frac{1}{n}\right)}\]

This problem is a part of this set .