Confused by this log question?

Question

Solve for x: log of x to the base of 1/√2 = -6

a) -8
b) 3.3 * 10^-9
c) 8
d) No solution

Answer 1

(1/√2)^(-6)=x
but 1/√2=1/(2^(1/2))=2^(-0.5)
so the first equation becomes (2^(-0.5))^(-6)=2^3=8
(C)

Answer 2

the base would be 1/(root2)
it would be raised to the (-6)power

negative exponents invert a fractional base....
so it becomes (root2)raised to the (+6) = 8

Answer 3

let a = 1 / √2
loga (x) = - 6
x = a^(- 6) =(1/√2)^( - 6) = (√2)^(6)
x = 8
ANSWER c)