How do you expand ${log (\frac{6}{11})}^{5}$ $log (6/11)^5$ ?

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Answer 1 · 2018-03-03T08:02:32

$5 log 6 - 5 log 11$ $5log6-5log11$

${log (\frac{6}{11})}^{5} = 5 log (\frac{6}{11})$ $log(6/11)^5 = 5 log(6/11)$ because ${log a}^{b} = b log a$ $log a^b = b log a$
$= 5 (log 6 - log 11)$ $=5(log 6 -log 11)$ because $log (\frac{a}{b}) = log a - log b$ $log(a/b)=log a - log b$
$= 5 log 6 - 5 log 11$ $=5log 6 -5log 11$ because $a (b - c) = a b - a c$ $a(b-c)=ab-ac$

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