How do you evaluate ${log}_{\frac{1}{2}} (\frac{1}{64})$ $log_(1/2) (1/64)$ ?

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Answer 1 · 2016-08-03T08:14:31

$6$ $6$

${log}_{\frac{1}{2}} (\frac{1}{64}) = {log}_{\frac{1}{2}} {(\frac{1}{2})}^{6} = 6$ $log_(1/2) (1/64) = log_{1/2}(1/2)^6=6$ because

${log}_{a} a^{b} = b$ $log_a a^b = b$

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