What is expand log_{8}(\sqrt[5]{(x^2y)/(64)}) ?

The solution to expand log_{8}(\sqrt[5]{(x^2y)/(64)}) is 1/5 log_{8}(x^2y)-2/5

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expand log_{8}(\sqrt[5]{(x^2y)/(64)})

expand

\frac{1}{5} lo g_{8} (x^{2} y) - \frac{2}{5}

Solution steps

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

Simplify

\frac{1}{5} lo g_{8} (x^{2} y) = \frac{1}{5} (lo g_{8} (y) + 2 lo g_{8} (x))

\frac{6}{5} lo g_{8} (2) = \frac{2}{5}

= \frac{1}{5} (2 lo g_{8} (x) + lo g_{8} (y)) - \frac{2}{5}

lo g_{8} (y) + 2 lo g_{8} (x) = lo g_{8} (y x^{2})

= \frac{1}{5} lo g_{8} (x^{2} y) - \frac{2}{5}

Simplify

lo g_{8} (x^{2} y) : 2 lo g_{8} (x) + lo g_{8} (y)

= \frac{1}{5} (2 lo g_{8} (x) + lo g_{8} (y)) - \frac{2}{5}

lo g_{8} (y) + 2 lo g_{8} (x) = lo g_{8} (y x^{2})

= \frac{1}{5} lo g_{8} (x^{2} y) - \frac{2}{5}

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(z - 1)^{2} (0.02 + \frac{0.05 ( z + 1 ) K}{( z - 1 ) ^{2}})

What is expand log_{8}(\sqrt[5]{(x^2y)/(64)}) ?
The solution to expand log_{8}(\sqrt[5]{(x^2y)/(64)}) is 1/5 log_{8}(x^2y)-2/5