What is expand log_{3}(\sqrt[5]{(x^4y)/9}) ?

The solution to expand log_{3}(\sqrt[5]{(x^4y)/9}) is -2/5+(log_{3}(y))/5+(4log_{3}(x))/5

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expand log_{3}(\sqrt[5]{(x^4y)/9})

expand

- \frac{2}{5} + \frac{lo g _{3} ( y )}{5} + \frac{4 lo g _{3} ( x )}{5}

Solution steps

Rewrite as

= lo g_{3} ((\frac{x ^{4} y}{9})^{\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_{3} (\frac{x ^{4} y}{9})

Simplify

lo g_{3} (\frac{x ^{4} y}{9}) : 4 lo g_{3} (x) + lo g_{3} (y) - 2

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

4 \cdot \frac{1}{5} lo g_{3} (x) = \frac{4}{5} lo g_{3} (x)

2 \cdot \frac{1}{5} = \frac{2}{5}

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

Multiply

\frac{1}{5} lo g_{3} (y) : \frac{lo g _{3} ( y )}{5}

= \frac{lo g _{3} ( y )}{5} + lo g_{3} (x) \frac{4}{5} - \frac{2}{5}

Multiply

lo g_{3} (x) \frac{4}{5} : \frac{4 lo g _{3} ( x )}{5}

= \frac{lo g _{3} ( y )}{5} + \frac{4 lo g _{3} ( x )}{5} - \frac{2}{5}

Combine the fractions

\frac{lo g _{3} ( y )}{5} + \frac{4 lo g _{3} ( x )}{5} : \frac{lo g _{3} ( y ) + 4 lo g _{3} ( x )}{5}

= - \frac{2}{5} + \frac{4 lo g _{3} ( x ) + lo g _{3} ( y )}{5}

Apply rule

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

= \frac{- 2 + lo g _{3} ( y ) + 4 lo g _{3} ( x )}{5}

- 2 + lo g_{3} (y) + 4 lo g_{3} (x) = - 2 + lo g_{3} (y x^{4})

= \frac{- 2 + lo g _{3} ( x ^{4} y )}{5}

lo g_{3} (y x^{4}) = lo g_{3} (y) + 4 lo g_{3} (x)

= \frac{- 2 + lo g _{3} ( y ) + 4 lo g _{3} ( x )}{5}

Apply the fraction rule:

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

\frac{- 2 + lo g _{3} ( y ) + 4 lo g _{3} ( x )}{5} = - \frac{2}{5} + \frac{lo g _{3} ( y )}{5} + \frac{4 lo g _{3} ( x )}{5}

= - \frac{2}{5} + \frac{lo g _{3} ( y )}{5} + \frac{4 lo g _{3} ( x )}{5}

\frac{3}{4 ( x + 8 )}

(3 + 2 cos (x))^{2}

(1 - e^{- 2 π s}) \cdot (\frac{A}{s} + \frac{B s + C}{s ^{2} + 1})

(\frac{x}{4} - \frac{1}{3}) (\frac{x}{4} + \frac{1}{3})

cos^{3} (y) (2 x sin (y) - cos^{3} (y))

What is expand log_{3}(\sqrt[5]{(x^4y)/9}) ?
The solution to expand log_{3}(\sqrt[5]{(x^4y)/9}) is -2/5+(log_{3}(y))/5+(4log_{3}(x))/5