What is expand log_{b}(\sqrt[5]{x/y}) ?

The solution to expand log_{b}(\sqrt[5]{x/y}) is 1/5 log_{b}(x/y)

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expand log_{b}(\sqrt[5]{x/y})

expand

\frac{1}{5} lo g_{b} (\frac{x}{y})

Solution steps

Rewrite as

= lo g_{b} ((\frac{x}{y})^{\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_{b} (\frac{x}{y})

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What is expand log_{b}(\sqrt[5]{x/y}) ?
The solution to expand log_{b}(\sqrt[5]{x/y}) is 1/5 log_{b}(x/y)