What is expand log_{7}(\sqrt[3]{(x^4y)/(49)}) ?

The solution to expand log_{7}(\sqrt[3]{(x^4y)/(49)}) is -2/3+(log_{7}(y))/3+(4log_{7}(x))/3

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expand log_{7}(\sqrt[3]{(x^4y)/(49)})

expand

- \frac{2}{3} + \frac{lo g _{7} ( y )}{3} + \frac{4 lo g _{7} ( x )}{3}

Solution steps

Rewrite as

= lo g_{7} ((\frac{x ^{4} y}{49})^{\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_{7} (\frac{x ^{4} y}{49})

Simplify

lo g_{7} (\frac{x ^{4} y}{49}) : 4 lo g_{7} (x) + lo g_{7} (y) - 2

= \frac{1}{3} (4 lo g_{7} (x) + lo g_{7} (y) - 2)

Distribute parentheses

= \frac{1}{3} lo g_{7} (y) + \frac{1}{3} \cdot 4 lo g_{7} (x) + \frac{1}{3} (- 2)

Apply minus-plus rules

+ (- a) = - a

= \frac{1}{3} lo g_{7} (y) + 4 \cdot \frac{1}{3} lo g_{7} (x) - 2 \cdot \frac{1}{3}

4 \cdot \frac{1}{3} lo g_{7} (x) = \frac{4}{3} lo g_{7} (x)

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

= \frac{1}{3} lo g_{7} (y) + \frac{4}{3} lo g_{7} (x) - \frac{2}{3}

Multiply

\frac{1}{3} lo g_{7} (y) : \frac{lo g _{7} ( y )}{3}

= \frac{lo g _{7} ( y )}{3} + lo g_{7} (x) \frac{4}{3} - \frac{2}{3}

Multiply

lo g_{7} (x) \frac{4}{3} : \frac{4 lo g _{7} ( x )}{3}

= \frac{lo g _{7} ( y )}{3} + \frac{4 lo g _{7} ( x )}{3} - \frac{2}{3}

Combine the fractions

\frac{lo g _{7} ( y )}{3} + \frac{4 lo g _{7} ( x )}{3} : \frac{lo g _{7} ( y ) + 4 lo g _{7} ( x )}{3}

= - \frac{2}{3} + \frac{4 lo g _{7} ( x ) + lo g _{7} ( y )}{3}

Apply rule

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

= \frac{- 2 + lo g _{7} ( y ) + 4 lo g _{7} ( x )}{3}

- 2 + lo g_{7} (y) + 4 lo g_{7} (x) = - 2 + lo g_{7} (y x^{4})

= \frac{- 2 + lo g _{7} ( x ^{4} y )}{3}

lo g_{7} (y x^{4}) = lo g_{7} (y) + 4 lo g_{7} (x)

= \frac{- 2 + lo g _{7} ( y ) + 4 lo g _{7} ( x )}{3}

Apply the fraction rule:

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

\frac{- 2 + lo g _{7} ( y ) + 4 lo g _{7} ( x )}{3} = - \frac{2}{3} + \frac{lo g _{7} ( y )}{3} + \frac{4 lo g _{7} ( x )}{3}

= - \frac{2}{3} + \frac{lo g _{7} ( y )}{3} + \frac{4 lo g _{7} ( x )}{3}

\frac{x + 4}{( x + 1 ) ^{2}}

(\frac{2 x}{y} - e^{x - y} + 1) (- \frac{2}{2})

(x - \frac{π}{2}) tan (x)

x y^{4} d x + (y^{2} + 2) e^{- 3 x} d y

(t - \frac{1}{4}) (t - \frac{3}{4})

What is expand log_{7}(\sqrt[3]{(x^4y)/(49)}) ?
The solution to expand log_{7}(\sqrt[3]{(x^4y)/(49)}) is -2/3+(log_{7}(y))/3+(4log_{7}(x))/3