What is 6log_{3}(y)-1/4 log_{3}(x)+2log_{3}(w) ?

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

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simplify 6log_{3}(y)-1/4 log_{3}(x)+2log_{3}(w)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= lo g_{3} (y^{6}) - \frac{1}{4} lo g_{3} (x) + 2 lo g_{3} (w)

Apply log rule:

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

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

= lo g_{3} (y^{6}) - lo g_{3} (x^{\frac{1}{4}}) + 2 lo g_{3} (w)

Apply log rule:

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

lo g_{3} (y^{6}) - lo g_{3} (x^{\frac{1}{4}}) = lo g_{3} (\frac{y ^{6}}{x ^{\frac{1}{4}}})

= lo g_{3} (\frac{y ^{6}}{x ^{\frac{1}{4}}}) + 2 lo g_{3} (w)

Simplify

\frac{y ^{6}}{x ^{\frac{1}{4}}} : \frac{y ^{6} x ^{\frac{3}{4}}}{x}

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

Apply log rule:

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

2 lo g_{3} (w) = lo g_{3} (w^{2})

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

Apply log rule:

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

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

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

Simplify

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

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

3 ln (\frac{13}{x})

ln (\frac{26}{\frac{7}{0.05}})

\frac{8}{13} lo g_{2} (\frac{8}{13}) - \frac{5}{13} lo g_{2} (\frac{5}{13})

0.18 - \frac{0.0591}{30} \cdot lo g_{10} (\frac{0.4}{0.2})

ln (\frac{4}{x}) + ln (\frac{2}{x ^{3}})

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