What is 3log_{6}(x)-1/5 log_{6}(y)+2log_{6}(w) ?

The solution to 3log_{6}(x)-1/5 log_{6}(y)+2log_{6}(w) is log_{6}((x^3w^2y^{4/5})/y)

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simplify 3log_{6}(x)-1/5 log_{6}(y)+2log_{6}(w)

simplify

3 lo g_{6} (x) - \frac{1}{5} lo g_{6} (y) + 2 lo g_{6} (w)

lo g_{6} (\frac{x ^{3} w ^{2} y ^{\frac{4}{5}}}{y})

Solution steps

3 lo g_{6} (x) - \frac{1}{5} lo g_{6} (y) + 2 lo g_{6} (w)

Apply log rule:

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

3 lo g_{6} (x) = lo g_{6} (x^{3})

= lo g_{6} (x^{3}) - \frac{1}{5} lo g_{6} (y) + 2 lo g_{6} (w)

Apply log rule:

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

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

= lo g_{6} (x^{3}) - lo g_{6} (y^{\frac{1}{5}}) + 2 lo g_{6} (w)

Apply log rule:

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

lo g_{6} (x^{3}) - lo g_{6} (y^{\frac{1}{5}}) = lo g_{6} (\frac{x ^{3}}{y ^{\frac{1}{5}}})

= lo g_{6} (\frac{x ^{3}}{y ^{\frac{1}{5}}}) + 2 lo g_{6} (w)

Simplify

\frac{x ^{3}}{y ^{\frac{1}{5}}} : \frac{x ^{3} y ^{\frac{4}{5}}}{y}

= lo g_{6} (\frac{x ^{3} y ^{\frac{4}{5}}}{y}) + 2 lo g_{6} (w)

Apply log rule:

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

2 lo g_{6} (w) = lo g_{6} (w^{2})

= lo g_{6} (\frac{x ^{3} y ^{\frac{4}{5}}}{y}) + lo g_{6} (w^{2})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{6} (\frac{x ^{3} y ^{\frac{4}{5}}}{y}) + lo g_{6} (w^{2}) = lo g_{6} (\frac{x ^{3} y ^{\frac{4}{5}}}{y} w^{2})

= lo g_{6} (\frac{x ^{3} y ^{\frac{4}{5}}}{y} w^{2})

Simplify

\frac{x ^{3} y ^{\frac{4}{5}}}{y} w^{2} : \frac{x ^{3} w ^{2} y ^{\frac{4}{5}}}{y}

= lo g_{6} (\frac{x ^{3} w ^{2} y ^{\frac{4}{5}}}{y})

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What is 3log_{6}(x)-1/5 log_{6}(y)+2log_{6}(w) ?
The solution to 3log_{6}(x)-1/5 log_{6}(y)+2log_{6}(w) is log_{6}((x^3w^2y^{4/5})/y)