Question

If Log x (1 / 8) = - 3 / 2, then x is equal to.

A. - 4
B. 4
C. 1 / 4
D: 0

Answer 1

`log_(x)(1/8)=-3/2`

This is equal to...

`x^(-3/2)=1/8`

We want "x" so we need to isolate it using laws of exponents...

`x^((-1)(3/2))=1/8`

`x^(3/2)=8` because
`x^(-a)=1/x^(a)`

`x=\sqrt[3]{8^(2)}` because
`x^(a/b)=\sqrt[b]{x^(a)}`

x = 4

answer: B