What is expand ln(\sqrt[3]{x^2}) ?

The solution to expand ln(\sqrt[3]{x^2}) is 2/3 ln(x)

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expand ln(\sqrt[3]{x^2})

expand

\frac{2}{3} ln (x)

Solution steps

Rewrite as

= ln ((x^{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} ln (x^{2})

Apply log rule

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

assuming

x \geq 0

= 2 \cdot \frac{1}{3} ln (x)

Multiply fractions:

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

= \frac{1 \cdot 2}{3} ln (x)

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{3} ln (x)

2 (u^{2} + v^{2}) 2 u^{2} + 2 v^{2} + 4

\frac{42 e ^{x} ( - 7 e ^{x} + 6 )}{( 7 e ^{x} + 6 ) ^{3}}

\frac{8}{( x + 4 ) ^{2}}

x δ (x - 2)

(x)^{2}

What is expand ln(\sqrt[3]{x^2}) ?
The solution to expand ln(\sqrt[3]{x^2}) is 2/3 ln(x)