What is 3log_{b}(y)-1/4 log_{b}(w)+2log_{b}(z) ?

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

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simplify 3log_{b}(y)-1/4 log_{b}(w)+2log_{b}(z)

simplify

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

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

Solution steps

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

Apply log rule:

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

3 lo g_{b} (y) = lo g_{b} (y^{3})

= lo g_{b} (y^{3}) - \frac{1}{4} lo g_{b} (w) + 2 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (y^{3}) - lo g_{b} (w^{\frac{1}{4}}) + 2 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (y^{3}) - lo g_{b} (w^{\frac{1}{4}}) = lo g_{b} (\frac{y ^{3}}{w ^{\frac{1}{4}}})

= lo g_{b} (\frac{y ^{3}}{w ^{\frac{1}{4}}}) + 2 lo g_{b} (z)

Simplify

\frac{y ^{3}}{w ^{\frac{1}{4}}} : \frac{y ^{3} w ^{\frac{3}{4}}}{w}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

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