The correct option is A 1−3log72
Let, L=log7(log7 √7(√7√7))
Let's simplify √7(√7√7) first.
√7(√7√7)=√7(√7×71/2)
=√7(√73/2)
=√7(73/2)1/2
=√7×73/4
=√77/4
=(77/4)1/2
=77/8
∴L=log7(log7 √7(√7√7))
=log7(log7 77/8)
=log7(78)
=log7 7−log7 8 =1−log7 23 =1−3log72