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 .

\frac{1}{n}

\log_{a}{n}

-\log_{a}{n}

None of these.

n-1