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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{6}}{w ^{\frac{1}{3}}} : \frac{x ^{6} w ^{\frac{2}{3}}}{w}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

ln (2 (x^{2} - 3 x + 2))

x (ln (c) - 5 ln (x))

3 ln (4) - 3 ln (3)

- \frac{1}{3} (lo g_{10} (155) - lo g_{10} (35.1))

ln (\frac{0.01 5 ^{2}}{0.01 1 ^{2}})

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