What is expand log_{10}(\sqrt[3]{z^2}) ?

The solution to expand log_{10}(\sqrt[3]{z^2}) is 2/3 log_{10}(z)

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expand log_{10}(\sqrt[3]{z^2})

expand

\frac{2}{3} lo g_{10} (z)

Solution steps

Rewrite as

= lo g_{10} ((z^{2})^{\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} (z^{2})

Apply log rule

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

assuming

x \geq 0

= 2 \cdot \frac{1}{3} lo g_{10} (z)

Multiply fractions:

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

= \frac{1 \cdot 2}{3} lo g_{10} (z)

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{3} lo g_{10} (z)

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What is expand log_{10}(\sqrt[3]{z^2}) ?
The solution to expand log_{10}(\sqrt[3]{z^2}) is 2/3 log_{10}(z)