It is not clear from the question, whether the base is 'x' or '10'. So I will solve it for both.
Assuming "x" is the base here,then log x (1/8) = -3/2 can be written as
1/8 = x^(-3/2) = 1/[x^(3/2)]
or x^(3/2) = 8 = 2^3
or, x = 2^(3/(3/2)) = 2^2 = 4
If base is "10", in that case: x(1/8) = 10^(-3/2)
or x = 8 * 10^(-3/2) = 0.253
Hope this helps.
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