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 =...

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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.