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

The solution to expand ln(\sqrt[3]{p^2q}) is 1/3 ln(q)+2/3 ln(p)

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

expand

\frac{1}{3} ln (q) + \frac{2}{3} ln (p)

Solution steps

Rewrite as

= ln ((p^{2} q)^{\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 (p^{2} q)

Simplify

ln (p^{2} q) : 2 ln (p) + ln (q)

= \frac{1}{3} (2 ln (p) + ln (q))

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{1}{3}, b = ln (q), c = 2 ln (p)

= \frac{1}{3} ln (q) + \frac{1}{3} \cdot 2 ln (p)

= \frac{1}{3} ln (q) + 2 \cdot \frac{1}{3} ln (p)

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

= \frac{1}{3} ln (q) + \frac{2}{3} ln (p)

e^{3 x} (e^{3 x} + 3 x e^{3 x})

(x + Δ x)^{2}

3 (3 + x)

\frac{1}{( s - 1 ) ^{4}}

(x + \frac{1}{2}) (x - 0) (x - \frac{1}{2})

What is expand ln(\sqrt[3]{p^2q}) ?
The solution to expand ln(\sqrt[3]{p^2q}) is 1/3 ln(q)+2/3 ln(p)