If log_0.5 64 = x, then the value of x is

1. -4

2. -6

3. 4

4. 6

Given,

log_0.5 64 = x

$\Rightarrow (0.5)^x = 64 \\[1em] \Rightarrow \Big(\dfrac{5}{10}\Big)^x = 64 \\[1em] \Rightarrow \Big(\dfrac{1}{2}\Big)^x = (2)^6 \\[1em] \Rightarrow (2^{-1})^x = (2)^6 \\[1em] \Rightarrow 2^{-x} = (2)^6 \\[1em] \Rightarrow -x = 6 \\[1em] \Rightarrow x = -6.$

Hence, Option 2 is the correct option.