I think log is outside the scope of GMAT.
One of my friend gave it to me. Couldn't get it done so thought of asking.
I just started quant so not aware of the scope per se
NEVERTHELESS, lets try and solve this
a^x = 1/8 = 2^(-3)
Since a is a perfect square ... a can be 4,9,16 etc. which gives different answers ... INSUFF
Simplifying .. gives
a = (8) (2^(2x/3) ) , x is unknown therefore ... INSUFF
Consider 1 and 2:
simplifying using logs we get 2 equations:
from 1: x log a = -3
from 2: log a = 2x/3 +3
eliminating log a gives: 2x^2 + 9x + 9 = 0 or x = -3 and -3/2
solving for a gives a = 2 or a = 4
since a is a perfect square .. a = 4 ... SUFFICIENT.