If logab = x then ax = b so if log1/√20.125 = x then 1/2x/2 =0.125
Now 0.125 = 1/8 = 1/23, so we must have x/2 = 3 or x = 6
Check
$${{log}}_{{\frac{{\mathtt{1}}}{{\sqrt{{\mathtt{2}}}}}}}{\left({\mathtt{0.125}}\right)} = {\mathtt{6.000\: \!000\: \!000\: \!000\: \!001}}$$
(The 1 at the end is just numerical error.)
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