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

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

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

expand

lo g_{4} (5 \frac{s ^{2} t}{16})

- \frac{2}{5} + \frac{lo g _{4} ( t )}{5} + \frac{2 lo g _{4} ( s )}{5}

Solution steps

lo g_{4} (5 \frac{s ^{2} t}{16})

Rewrite as

= lo g_{4} ((\frac{s ^{2} t}{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_{4} (\frac{s ^{2} t}{16})

Simplify

lo g_{4} (\frac{s ^{2} t}{16}) : 2 lo g_{4} (s) + lo g_{4} (t) - 2

= \frac{1}{5} (2 lo g_{4} (s) + lo g_{4} (t) - 2)

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

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

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

= \frac{1}{5} lo g_{4} (t) + \frac{2}{5} lo g_{4} (s) - \frac{2}{5}

Multiply

\frac{1}{5} lo g_{4} (t) : \frac{lo g _{4} ( t )}{5}

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

Multiply

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

= \frac{lo g _{4} ( t )}{5} + \frac{2 lo g _{4} ( s )}{5} - \frac{2}{5}

Combine the fractions

\frac{lo g _{4} ( t )}{5} + \frac{2 lo g _{4} ( s )}{5} : \frac{lo g _{4} ( t ) + 2 lo g _{4} ( s )}{5}

= - \frac{2}{5} + \frac{2 lo g _{4} ( s ) + lo g _{4} ( t )}{5}

Apply rule

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

= \frac{- 2 + lo g _{4} ( t ) + 2 lo g _{4} ( s )}{5}

- 2 + lo g_{4} (t) + 2 lo g_{4} (s) = - 2 + lo g_{4} (t s^{2})

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

lo g_{4} (t s^{2}) = lo g_{4} (t) + 2 lo g_{4} (s)

= \frac{- 2 + lo g _{4} ( t ) + 2 lo g _{4} ( s )}{5}

Apply the fraction rule:

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

\frac{- 2 + lo g _{4} ( t ) + 2 lo g _{4} ( s )}{5} = - \frac{2}{5} + \frac{lo g _{4} ( t )}{5} + \frac{2 lo g _{4} ( s )}{5}

= - \frac{2}{5} + \frac{lo g _{4} ( t )}{5} + \frac{2 lo g _{4} ( s )}{5}

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