Logarithms' challenger #2

Algebra Level 3

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

This problem is a part of this set .

-\log_{a}{n}

\frac{1}{n}

1 None of these.

n-1

\log_{a}{n}