What is 1/4 log_{6}(w)+2log_{6}(y)-log_{6}(x) ?

The solution to 1/4 log_{6}(w)+2log_{6}(y)-log_{6}(x) is log_{6}((\sqrt[4]{w}y^2)/x)

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simplify 1/4 log_{6}(w)+2log_{6}(y)-log_{6}(x)

simplify

\frac{1}{4} lo g_{6} (w) + 2 lo g_{6} (y) - lo g_{6} (x)

Solution steps

\frac{1}{4} lo g_{6} (w) + 2 lo g_{6} (y) - lo g_{6} (x)

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

2 lo g_{6} (y) = lo g_{6} (y^{2})

= lo g_{6} (w^{\frac{1}{4}}) + lo g_{6} (y^{2}) - lo g_{6} (x)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{6} (w^{\frac{1}{4}}) + lo g_{6} (y^{2}) = lo g_{6} (w^{\frac{1}{4}} y^{2})

= lo g_{6} (w^{\frac{1}{4}} y^{2}) - lo g_{6} (x)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{6} (w^{\frac{1}{4}} y^{2}) - lo g_{6} (x) = lo g_{6} (\frac{w ^{\frac{1}{4}} y ^{2}}{x})

= lo g_{6} (\frac{w ^{\frac{1}{4}} y ^{2}}{x})

Apply exponent rule:

lo g_{6} (\frac{36}{x + 1})

lo g_{10} (a + b) + lo g_{10} (a - b)

4 lo g_{b} (x + 2) - \frac{1}{3} lo g_{b} (x - 5)

ln (\frac{4 m ^{5}}{p})

ln (\frac{x ^{3}}{y ^{2}})

What is 1/4 log_{6}(w)+2log_{6}(y)-log_{6}(x) ?
The solution to 1/4 log_{6}(w)+2log_{6}(y)-log_{6}(x) is log_{6}((\sqrt[4]{w}y^2)/x)