What is expand log_{10}(\sqrt[3]{m/n}) ?

The solution to expand log_{10}(\sqrt[3]{m/n}) is 1/3 log_{10}(m/n)

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expand log_{10}(\sqrt[3]{m/n})

expand

\frac{1}{3} lo g_{10} (\frac{m}{n})

Solution steps

Rewrite as

= lo g_{10} ((\frac{m}{n})^{\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_{10} (\frac{m}{n})

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What is expand log_{10}(\sqrt[3]{m/n}) ?
The solution to expand log_{10}(\sqrt[3]{m/n}) is 1/3 log_{10}(m/n)