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}

(5 x^{3} - x) (\frac{1}{x ^{2}} - 3)

\frac{( 33 x + 895 ) ^{2}}{42432196 ( 11 x ^{2} + 5 x + 6 )}

sin (π (1 - n))

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

\frac{3}{4} (6 ln (6) + 5)

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