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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

4 lo g_{6} (x) = lo g_{6} (x^{4})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{4}}{y ^{\frac{1}{3}}} : \frac{x ^{4} y ^{\frac{2}{3}}}{y}

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

lo g_{7} ((x y z^{2})^{3})

5 ln ∣ x + 3 ∣ - \frac{8}{x + 3} + 5 ln ∣ x + 7 ∣

ln (e^{x} \cdot x)

lo g_{10} (\frac{g j ^{5} k}{100})

ln (\frac{5}{2})

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