TMUA 2019 · Paper 2 · Question 15

The numbers $a$ , $b$ and $c$ are each greater than $1$ .

The following logarithms are all to the same base:

lo g (a b^{2} c) = 7

lo g (a^{2} b c^{2}) = 11

lo g (a^{2} b^{2} c^{3}) = 15

What is this base?