How do you evaluate ${log}_{6} (144) - {log}_{6} (4)$ $log_[6](144) - log_[6](4)$ ?

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How do you evaluate ${log}_{6} (144) - {log}_{6} (4)$ $log_[6](144) - log_[6](4)$ ?

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Answer 1 · 2016-04-04T01:41:33

${log}_{6} (144) - {log}_{6} (4) = 2$ $log_6(144) - log_6(4) = 2$

Explanation:

Use the identity

${log}_{x} (a) - {log}_{x} (b) = {log}_{x} (\frac{a}{b})$ $log_x(a) - log_x(b) = log_x(a/b)$

Thus,

${log}_{6} (144) - {log}_{6} (4) = {log}_{6} (\frac{144}{4})$ $log_6(144) - log_6(4) = log_6(144/4)$

$= {log}_{6} (36)$ $= log_6(36)$

$= {log}_{6} (6^{2})$ $= log_6(6^2)$

$= 2$ $= 2$

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How do you evaluate ${log}_{6} (144) - {log}_{6} (4)$ $log_[6](144) - log_[6](4)$ ?

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