What is 3log_{m}(z)-1/5 log_{m}(w)+6log_{m}(x) ?

The solution to 3log_{m}(z)-1/5 log_{m}(w)+6log_{m}(x) is log_{m}((z^3x^6w^{4/5})/w)

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simplify 3log_{m}(z)-1/5 log_{m}(w)+6log_{m}(x)

simplify

3 lo g_{m} (z) - \frac{1}{5} lo g_{m} (w) + 6 lo g_{m} (x)

lo g_{m} (\frac{z ^{3} x ^{6} w ^{\frac{4}{5}}}{w})

Solution steps

3 lo g_{m} (z) - \frac{1}{5} lo g_{m} (w) + 6 lo g_{m} (x)

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} (z^{3}) - \frac{1}{5} lo g_{m} (w) + 6 lo g_{m} (x)

Apply log rule:

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

\frac{1}{5} lo g_{m} (w) = lo g_{m} (w^{\frac{1}{5}})

= lo g_{m} (z^{3}) - lo g_{m} (w^{\frac{1}{5}}) + 6 lo g_{m} (x)

Apply log rule:

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

lo g_{m} (z^{3}) - lo g_{m} (w^{\frac{1}{5}}) = lo g_{m} (\frac{z ^{3}}{w ^{\frac{1}{5}}})

= lo g_{m} (\frac{z ^{3}}{w ^{\frac{1}{5}}}) + 6 lo g_{m} (x)

Simplify

\frac{z ^{3}}{w ^{\frac{1}{5}}} : \frac{z ^{3} w ^{\frac{4}{5}}}{w}

= lo g_{m} (\frac{z ^{3} w ^{\frac{4}{5}}}{w}) + 6 lo g_{m} (x)

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} (\frac{z ^{3} w ^{\frac{4}{5}}}{w}) + lo g_{m} (x^{6})

Apply log rule:

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

lo g_{m} (\frac{z ^{3} w ^{\frac{4}{5}}}{w}) + lo g_{m} (x^{6}) = lo g_{m} (\frac{z ^{3} w ^{\frac{4}{5}}}{w} x^{6})

= lo g_{m} (\frac{z ^{3} w ^{\frac{4}{5}}}{w} x^{6})

Simplify

\frac{z ^{3} w ^{\frac{4}{5}}}{w} x^{6} : \frac{z ^{3} x ^{6} w ^{\frac{4}{5}}}{w}

= lo g_{m} (\frac{z ^{3} x ^{6} w ^{\frac{4}{5}}}{w})

x^{l o g_{x} ((x + 3)^{2}) = 16}

ln (a) + 2 ln (b)

ln (x) - ln (1 - x)

\frac{ln ( \frac{8}{5} )}{2 ln ( 5 )}

- \frac{1}{0.19} ln (\frac{2}{11})

What is 3log_{m}(z)-1/5 log_{m}(w)+6log_{m}(x) ?
The solution to 3log_{m}(z)-1/5 log_{m}(w)+6log_{m}(x) is log_{m}((z^3x^6w^{4/5})/w)