What is 1/5 log_{4}(w)+4log_{4}(z)-log_{4}(y) ?

The solution to 1/5 log_{4}(w)+4log_{4}(z)-log_{4}(y) is log_{4}((\sqrt[5]{w}z^4)/y)

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simplify 1/5 log_{4}(w)+4log_{4}(z)-log_{4}(y)

simplify

\frac{1}{5} lo g_{4} (w) + 4 lo g_{4} (z) - lo g_{4} (y)

Solution steps

\frac{1}{5} lo g_{4} (w) + 4 lo g_{4} (z) - lo g_{4} (y)

\frac{1}{5} lo g_{4} (w) = lo g_{4} (w^{\frac{1}{5}})

4 lo g_{4} (z) = lo g_{4} (z^{4})

= lo g_{4} (w^{\frac{1}{5}}) + lo g_{4} (z^{4}) - lo g_{4} (y)

Apply log rule:

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

lo g_{4} (w^{\frac{1}{5}}) + lo g_{4} (z^{4}) = lo g_{4} (w^{\frac{1}{5}} z^{4})

= lo g_{4} (w^{\frac{1}{5}} z^{4}) - lo g_{4} (y)

Apply log rule:

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

lo g_{4} (w^{\frac{1}{5}} z^{4}) - lo g_{4} (y) = lo g_{4} (\frac{w ^{\frac{1}{5}} z ^{4}}{y})

= lo g_{4} (\frac{w ^{\frac{1}{5}} z ^{4}}{y})

Apply exponent rule:

ln (x^{7} 5 - x)

800 ln (10) - 480 ln (6) - 320

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (5)

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

lo g_{2} (\frac{8}{x + 4})

What is 1/5 log_{4}(w)+4log_{4}(z)-log_{4}(y) ?
The solution to 1/5 log_{4}(w)+4log_{4}(z)-log_{4}(y) is log_{4}((\sqrt[5]{w}z^4)/y)