If $\text{log}_{\sqrt[3]{5}} \space x$ = -3, then the value of x is

1. $\dfrac{1}{5}$

2. $-\dfrac{1}{5}$

3. -1

4. 5

Given,

$\Rightarrow \text{log}_{\sqrt[3]{5}} \space x = -3 \\[1em] \Rightarrow x = (\sqrt[3]{5})^{-3} \\[1em] \Rightarrow x = [(5)^{\dfrac{1}{3}}]^{-3} \\[1em] \Rightarrow x = (5)^{\dfrac{1}{3} \times (-3)} \\[1em] \Rightarrow x = (5)^{-1} = \dfrac{1}{5}.$

Hence, Option 1 is the correct option.