How do you evaluate ${log}_{\frac{1}{3}} (\frac{1}{27})$ $log_(1/3) (1/27)$ ?

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How do you evaluate ${log}_{\frac{1}{3}} (\frac{1}{27})$ $log_(1/3) (1/27)$ ?

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Answer 1 · 2016-10-01T04:02:22

$3$ $3$

Explanation:

${log}_{\frac{1}{3}} (\frac{1}{27})$ $log_(1/3)(1/27)$
$= {log}_{\frac{1}{3}} {(\frac{1}{3})}^{3}$ $=log_(1/3)(1/3)^3$
$= 3 {log}_{\frac{1}{3}} (\frac{1}{3})$ $=3log_(1/3)(1/3)$
$= 3$ $=3$

Alternatively, you can do it this way :

Recall that ${log}_{a} b = c, \Rightarrow a^{c} = b$ $log_ab=c, =>a^c=b$

let ${log}_{\frac{1}{3}} (\frac{1}{27}) = x$ $log_(1/3)(1/27)=x$
$\Rightarrow {(\frac{1}{3})}^{x} = \frac{1}{27} = {(\frac{1}{3})}^{3}$ $=> (1/3)^x=1/27=(1/3)^3$
Hence, $x = 3$ $x=3$

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Explanation:

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