Question

Determine log 256 base 1÷2 =x

Answer 1

x = log₁/₂ 256 = log₀.₅256

Using the change of base formula,

log₀.₅256 = log 256 / log 0.5 = -8

Answer 2

Hey friend
here is your answer

$if \: \: \: \: log_{ \frac{1}{2} }(256) = x \\ then \\ { (\frac{1}{2} )}^{x} = 256 \\ {( \frac{1}{2}) }^{x} = { (\frac{1}{2} )}^{ - 8} \\ comparing \: both \: sides \: \\ x = - 8$

so, final value of x = -8


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