What is 3log_{a}(x)-1/4 log_{a}(w)+7log_{a}(y) ?

The solution to 3log_{a}(x)-1/4 log_{a}(w)+7log_{a}(y) is log_{a}((x^3y^7w^{3/4})/w)

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simplify 3log_{a}(x)-1/4 log_{a}(w)+7log_{a}(y)

simplify

3 lo g_{a} (x) - \frac{1}{4} lo g_{a} (w) + 7 lo g_{a} (y)

lo g_{a} (\frac{x ^{3} y ^{7} w ^{\frac{3}{4}}}{w})

Solution steps

3 lo g_{a} (x) - \frac{1}{4} lo g_{a} (w) + 7 lo g_{a} (y)

Apply log rule:

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

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

= lo g_{a} (x^{3}) - \frac{1}{4} lo g_{a} (w) + 7 lo g_{a} (y)

Apply log rule:

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

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

= lo g_{a} (x^{3}) - lo g_{a} (w^{\frac{1}{4}}) + 7 lo g_{a} (y)

Apply log rule:

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

lo g_{a} (x^{3}) - lo g_{a} (w^{\frac{1}{4}}) = lo g_{a} (\frac{x ^{3}}{w ^{\frac{1}{4}}})

= lo g_{a} (\frac{x ^{3}}{w ^{\frac{1}{4}}}) + 7 lo g_{a} (y)

Simplify

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

= lo g_{a} (\frac{x ^{3} w ^{\frac{3}{4}}}{w}) + 7 lo g_{a} (y)

Apply log rule:

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

7 lo g_{a} (y) = lo g_{a} (y^{7})

= lo g_{a} (\frac{x ^{3} w ^{\frac{3}{4}}}{w}) + lo g_{a} (y^{7})

Apply log rule:

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

lo g_{a} (\frac{x ^{3} w ^{\frac{3}{4}}}{w}) + lo g_{a} (y^{7}) = lo g_{a} (\frac{x ^{3} w ^{\frac{3}{4}}}{w} y^{7})

= lo g_{a} (\frac{x ^{3} w ^{\frac{3}{4}}}{w} y^{7})

Simplify

\frac{x ^{3} w ^{\frac{3}{4}}}{w} y^{7} : \frac{x ^{3} y ^{7} w ^{\frac{3}{4}}}{w}

= lo g_{a} (\frac{x ^{3} y ^{7} w ^{\frac{3}{4}}}{w})

- ln (7 e^{- x})

3 ln (pq) + 4 ln (p q^{2})

lo g_{e} (\frac{5204}{5101})

lo g_{10} (2 π \cdot 802 \cdot 5.03 \cdot 9.566)

ln (156 e^{5})

What is 3log_{a}(x)-1/4 log_{a}(w)+7log_{a}(y) ?
The solution to 3log_{a}(x)-1/4 log_{a}(w)+7log_{a}(y) is log_{a}((x^3y^7w^{3/4})/w)