Expert Answers

An illustration of the letter 'A' in a speech bubbles

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 =...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

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.

Approved by eNotes Editorial Team