What is 2log_{6}(z)-1/4 log_{6}(w)+6log_{6}(y) ?

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

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simplify 2log_{6}(z)-1/4 log_{6}(w)+6log_{6}(y)

simplify

2 lo g_{6} (z) - \frac{1}{4} lo g_{6} (w) + 6 lo g_{6} (y)

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

Solution steps

2 lo g_{6} (z) - \frac{1}{4} lo g_{6} (w) + 6 lo g_{6} (y)

Apply log rule:

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

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

= lo g_{6} (z^{2}) - \frac{1}{4} lo g_{6} (w) + 6 lo g_{6} (y)

Apply log rule:

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

\frac{1}{4} lo g_{6} (w) = lo g_{6} (w^{\frac{1}{4}})

= lo g_{6} (z^{2}) - lo g_{6} (w^{\frac{1}{4}}) + 6 lo g_{6} (y)

Apply log rule:

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

lo g_{6} (z^{2}) - lo g_{6} (w^{\frac{1}{4}}) = lo g_{6} (\frac{z ^{2}}{w ^{\frac{1}{4}}})

= lo g_{6} (\frac{z ^{2}}{w ^{\frac{1}{4}}}) + 6 lo g_{6} (y)

Simplify

\frac{z ^{2}}{w ^{\frac{1}{4}}} : \frac{z ^{2} w ^{\frac{3}{4}}}{w}

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

Apply log rule:

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

6 lo g_{6} (y) = lo g_{6} (y^{6})

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

Apply log rule:

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

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

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

Simplify

\frac{z ^{2} w ^{\frac{3}{4}}}{w} y^{6} : \frac{z ^{2} y ^{6} w ^{\frac{3}{4}}}{w}

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

- 3 ln (2) + ln (3)

lo g_{2} (x^{9})

ln (\frac{6}{10})

\frac{1}{2} ln (2 v^{2} + 1) - ln (v^{2} + 1)

3 lo g_{b} (q) + 6 lo g_{b} (v)

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