Evaluate log₂ (1 ÷ 8)

Let,

$\Rightarrow \text{log}_{2} \space (1 ÷ 8) = x \\[1em] \Rightarrow 1 ÷ 8 = 2^x \\[1em] \Rightarrow \dfrac{1}{8} = 2^x \\[1em] \Rightarrow \dfrac{1}{2^3} = 2^x \\[1em] \Rightarrow 2^{-3} = 2^x \\[1em] \Rightarrow x = -3.$

Hence, log₂ (1 ÷ 8) = -3.