What is log_{b}(\sqrt[5]{(xy^2)/(z^3)}) ?

The solution to log_{b}(\sqrt[5]{(xy^2)/(z^3)}) is 1/5 (log_{b}(xy^2)-3log_{b}(z))

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simplify log_{b}(\sqrt[5]{(xy^2)/(z^3)})

simplify

\frac{1}{5} (lo g_{b} (x y^{2}) - 3 lo g_{b} (z))

Solution steps

Rewrite as

= lo g_{b} ((\frac{x y ^{2}}{z ^{3}})^{\frac{1}{5}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{5} lo g_{b} (\frac{x y ^{2}}{z ^{3}})

Simplify

lo g_{b} (\frac{x y ^{2}}{z ^{3}}) : - 3 lo g_{b} (z) + lo g_{b} (x y^{2})

= \frac{1}{5} (- 3 lo g_{b} (z) + lo g_{b} (x y^{2}))

(a^{2} + 2 b)^{3}

\frac{2}{5} - \frac{2}{5}

(1 - x^{2})^{5}

(3 x^{2} - 6 x + 11) - (10 x^{2} - 4 x + 6)

\frac{24 z + 13}{z ^{2} - 100} - \frac{23 z + 3}{z ^{2} - 100}

What is log_{b}(\sqrt[5]{(xy^2)/(z^3)}) ?
The solution to log_{b}(\sqrt[5]{(xy^2)/(z^3)}) is 1/5 (log_{b}(xy^2)-3log_{b}(z))