The value of $\text{log}_{\sqrt{2}} \space 8$ is :

1. 6

2. 4

3. 3

4. 8

Let value of $\text{log}_{\sqrt{2}} \space 8$ be x.

$\therefore \text{log}_{\sqrt{2}} \space 8 = x \\[1em] \Rightarrow (\sqrt{2})^x = 8 \\[1em] \Rightarrow (\sqrt{2})^x = (\sqrt{2})^6 \\[1em] \Rightarrow x = 6.$

Hence, Option 1 is the correct option.