What is expand log_{10}(\sqrt[4]{x^3}) ?

The solution to expand log_{10}(\sqrt[4]{x^3}) is 3/4 log_{10}(x)

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expand log_{10}(\sqrt[4]{x^3})

expand

\frac{3}{4} lo g_{10} (x)

Solution steps

Rewrite as

= lo g_{10} ((x^{3})^{\frac{1}{4}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{4} lo g_{10} (x^{3})

Apply log rule

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

assuming

x \geq 0

= 3 \cdot \frac{1}{4} lo g_{10} (x)

Multiply fractions:

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

= \frac{1 \cdot 3}{4} lo g_{10} (x)

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{4} lo g_{10} (x)

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What is expand log_{10}(\sqrt[4]{x^3}) ?
The solution to expand log_{10}(\sqrt[4]{x^3}) is 3/4 log_{10}(x)