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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

\frac{1}{4} lo g_{6} (z) = lo g_{6} (z^{\frac{1}{4}})

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

Apply log rule:

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

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

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

Simplify

\frac{y ^{4}}{z ^{\frac{1}{4}}} : \frac{y ^{4} z ^{\frac{3}{4}}}{z}

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

lo g_{10} (2) + lo g_{10} (8) - lo g_{10} (4)

lo g_{10} (\frac{x}{2})

lo g_{10} (\frac{z ^{3}}{x ^{5} y})

ln (\frac{e ^{x l n (2)}}{2})

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