What is expand log_{2}(\sqrt[5]{(xy^4)/(16)}) ?

The solution to expand log_{2}(\sqrt[5]{(xy^4)/(16)}) is -4/5+(log_{2}(x))/5+(4log_{2}(y))/5

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expand log_{2}(\sqrt[5]{(xy^4)/(16)})

expand

- \frac{4}{5} + \frac{lo g _{2} ( x )}{5} + \frac{4 lo g _{2} ( y )}{5}

Solution steps

Rewrite as

= lo g_{2} ((\frac{x y ^{4}}{16})^{\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_{2} (\frac{x y ^{4}}{16})

Simplify

lo g_{2} (\frac{x y ^{4}}{16}) : lo g_{2} (x) + 4 lo g_{2} (y) - 4

= \frac{1}{5} (lo g_{2} (x) + 4 lo g_{2} (y) - 4)

Distribute parentheses

= \frac{1}{5} lo g_{2} (x) + \frac{1}{5} \cdot 4 lo g_{2} (y) + \frac{1}{5} (- 4)

Apply minus-plus rules

+ (- a) = - a

= \frac{1}{5} lo g_{2} (x) + 4 \cdot \frac{1}{5} lo g_{2} (y) - 4 \cdot \frac{1}{5}

4 \cdot \frac{1}{5} lo g_{2} (y) = \frac{4}{5} lo g_{2} (y)

4 \cdot \frac{1}{5} = \frac{4}{5}

= \frac{1}{5} lo g_{2} (x) + \frac{4}{5} lo g_{2} (y) - \frac{4}{5}

Multiply

\frac{1}{5} lo g_{2} (x) : \frac{lo g _{2} ( x )}{5}

= \frac{lo g _{2} ( x )}{5} + lo g_{2} (y) \frac{4}{5} - \frac{4}{5}

Multiply

lo g_{2} (y) \frac{4}{5} : \frac{4 lo g _{2} ( y )}{5}

= \frac{lo g _{2} ( x )}{5} + \frac{4 lo g _{2} ( y )}{5} - \frac{4}{5}

Combine the fractions

\frac{lo g _{2} ( x )}{5} + \frac{4 lo g _{2} ( y )}{5} : \frac{lo g _{2} ( x ) + 4 lo g _{2} ( y )}{5}

= - \frac{4}{5} + \frac{lo g _{2} ( x ) + 4 lo g _{2} ( y )}{5}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 4 + lo g _{2} ( x ) + 4 lo g _{2} ( y )}{5}

- 4 + lo g_{2} (x) + 4 lo g_{2} (y) = - 4 + lo g_{2} (x y^{4})

= \frac{- 4 + lo g _{2} ( x y ^{4} )}{5}

lo g_{2} (x y^{4}) = lo g_{2} (x) + 4 lo g_{2} (y)

= \frac{- 4 + lo g _{2} ( x ) + 4 lo g _{2} ( y )}{5}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 4 + lo g _{2} ( x ) + 4 lo g _{2} ( y )}{5} = - \frac{4}{5} + \frac{lo g _{2} ( x )}{5} + \frac{4 lo g _{2} ( y )}{5}

= - \frac{4}{5} + \frac{lo g _{2} ( x )}{5} + \frac{4 lo g _{2} ( y )}{5}

x^{\frac{1}{2}} (x + 1)

x + (y - 2 x) y^{'} (x)

e^{θ} (- θt + \frac{t ^{2}}{2})

x^{\frac{2}{5}} (x - 5)

(2, - 12) y (6, 1)

What is expand log_{2}(\sqrt[5]{(xy^4)/(16)}) ?
The solution to expand log_{2}(\sqrt[5]{(xy^4)/(16)}) is -4/5+(log_{2}(x))/5+(4log_{2}(y))/5