How do you evaluate ${log}_{\frac{1}{5}} (\frac{1}{125})$ $log_(1/5) (1/125)$ ?

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How do you evaluate ${log}_{\frac{1}{5}} (\frac{1}{125})$ $log_(1/5) (1/125)$ ?

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Answer 1 · 2016-08-23T12:47:42

3

Explanation:

${log}_{\frac{1}{5}} (\frac{1}{125}) = {log}_{\frac{1}{5}} (\frac{1}{5^{3}}) = {log}_{\frac{1}{5}} {(\frac{1}{5})}^{3}$ $log_(1/5) (1/125) = log_(1/5) (1/5^3) = log_(1/5) (1/5)^3$

$= 3 {log}_{\frac{1}{5}} (\frac{1}{5})$ $= 3log_(1/5) (1/5)$

$= 3$ $=3$

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How do you evaluate ${log}_{\frac{1}{5}} (\frac{1}{125})$ $log_(1/5) (1/125)$ ?

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