The relation $\sqrt[3]{64} = 4$ in logarithmic form is:

1. log₆₄ 4 = 3

2. $\log_4 \space 64 = \dfrac{1}{3}$

3. $\log_{64} \space 4 = \dfrac{1}{3}$

4. $\log_{64} \space \dfrac{1}{3} = 4$

Given,

$\Rightarrow \sqrt[3]{64} = 4 \\[1em] \Rightarrow (64)^{\dfrac{1}{3}} = 4 \\[1em] \Rightarrow \log_{64} \space 4 = \dfrac{1}{3}.$

Hence, option 3 is the correct option.