What is 1/5 log_{6}(b-6)-2/5 log_{6}(b) ?

The solution to 1/5 log_{6}(b-6)-2/5 log_{6}(b) is log_{6}(\sqrt[5]{(b-6)/(b^2)})

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simplify 1/5 log_{6}(b-6)-2/5 log_{6}(b)

simplify

\frac{1}{5} lo g_{6} (b - 6) - \frac{2}{5} lo g_{6} (b)

Solution steps

\frac{1}{5} lo g_{6} (b - 6) - \frac{2}{5} lo g_{6} (b)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{5} lo g_{6} (b - 6) = lo g_{6} ((b - 6)^{\frac{1}{5}})

= lo g_{6} ((b - 6)^{\frac{1}{5}}) - \frac{2}{5} lo g_{6} (b)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{2}{5} lo g_{6} (b) = lo g_{6} (b^{\frac{2}{5}})

= lo g_{6} ((b - 6)^{\frac{1}{5}}) - lo g_{6} (b^{\frac{2}{5}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{6} ((b - 6)^{\frac{1}{5}}) - lo g_{6} (b^{\frac{2}{5}}) = lo g_{6} (\frac{( b - 6 ) ^{\frac{1}{5}}}{b ^{\frac{2}{5}}})

= lo g_{6} (\frac{( b - 6 ) ^{\frac{1}{5}}}{b ^{\frac{2}{5}}})

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What is 1/5 log_{6}(b-6)-2/5 log_{6}(b) ?
The solution to 1/5 log_{6}(b-6)-2/5 log_{6}(b) is log_{6}(\sqrt[5]{(b-6)/(b^2)})