What is expand ln(\sqrt[5]{(yz)/(x^6)}) ?

The solution to expand ln(\sqrt[5]{(yz)/(x^6)}) is 1/5 ln(yz)-6/5 ln(x)

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expand ln(\sqrt[5]{(yz)/(x^6)})

expand

\frac{1}{5} ln (yz) - \frac{6}{5} ln (x)

Solution steps

Rewrite as

= ln ((\frac{yz}{x ^{6}})^{\frac{1}{5}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{5} ln (\frac{yz}{x ^{6}})

Simplify

ln (\frac{yz}{x ^{6}}) : - 6 ln (x) + ln (yz)

= \frac{1}{5} (- 6 ln (x) + ln (yz))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{5}, b = ln (yz), c = 6 ln (x)

= \frac{1}{5} ln (yz) - \frac{1}{5} \cdot 6 ln (x)

= \frac{1}{5} ln (yz) - 6 \cdot \frac{1}{5} ln (x)

6 \cdot \frac{1}{5} ln (x) = \frac{6}{5} ln (x)

= \frac{1}{5} ln (yz) - \frac{6}{5} ln (x)

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What is expand ln(\sqrt[5]{(yz)/(x^6)}) ?
The solution to expand ln(\sqrt[5]{(yz)/(x^6)}) is 1/5 ln(yz)-6/5 ln(x)