What is expand log_{10}(\sqrt[8]{x/z}) ?

The solution to expand log_{10}(\sqrt[8]{x/z}) is 1/8 log_{10}(x/z)

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expand log_{10}(\sqrt[8]{x/z})

expand

\frac{1}{8} lo g_{10} (\frac{x}{z})

Solution steps

Rewrite as

= lo g_{10} ((\frac{x}{z})^{\frac{1}{8}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{8} lo g_{10} (\frac{x}{z})

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What is expand log_{10}(\sqrt[8]{x/z}) ?
The solution to expand log_{10}(\sqrt[8]{x/z}) is 1/8 log_{10}(x/z)