What is expand log_{5}(\sqrt[3]{(x^2y)/(25)}) ?

The solution to expand log_{5}(\sqrt[3]{(x^2y)/(25)}) is -2/3+(log_{5}(y))/3+(2log_{5}(x))/3

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expand log_{5}(\sqrt[3]{(x^2y)/(25)})

expand

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

Solution steps

Rewrite as

= lo g_{5} ((\frac{x ^{2} y}{25})^{\frac{1}{3}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{3} lo g_{5} (\frac{x ^{2} y}{25})

Simplify

lo g_{5} (\frac{x ^{2} y}{25}) : 2 lo g_{5} (x) + lo g_{5} (y) - 2

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

2 \cdot \frac{1}{3} lo g_{5} (x) = \frac{2}{3} lo g_{5} (x)

2 \cdot \frac{1}{3} = \frac{2}{3}

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

Multiply

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

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

Multiply

lo g_{5} (x) \frac{2}{3} : \frac{2 lo g _{5} ( x )}{3}

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

Combine the fractions

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

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

Apply rule

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

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

- 2 + lo g_{5} (y) + 2 lo g_{5} (x) = - 2 + lo g_{5} (y x^{2})

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

lo g_{5} (y x^{2}) = lo g_{5} (y) + 2 lo g_{5} (x)

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

Apply the fraction rule:

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

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

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

\frac{( - 4 y + 1 ) ( 12 x ^{2} - 8 x y - 6 x + 16 y ^{2} + 4 y + 1 )}{8}

(9 x - 2) e^{5 x}

\frac{( - 10 x ^{2} + 160 x )}{( 5 x ^{2} - 2 x + 16 ) ^{2}}

(a + b \cdot cos (t))^{3}

95 (1 + 3)

What is expand log_{5}(\sqrt[3]{(x^2y)/(25)}) ?
The solution to expand log_{5}(\sqrt[3]{(x^2y)/(25)}) is -2/3+(log_{5}(y))/3+(2log_{5}(x))/3