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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{y ^{3}}{x ^{\frac{1}{3}}} : \frac{y ^{3} x ^{\frac{2}{3}}}{x}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

ln (\frac{x + 3}{x + 1})

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

ln (\frac{10}{627.6 8 ^{2}})

lo g_{2} (\frac{n}{e})

lo g_{4} (4^{x} sin^{2} (x))

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