What is expand log_{7}(\sqrt[3]{x^5}) ?

The solution to expand log_{7}(\sqrt[3]{x^5}) is 5/3 log_{7}(x)

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expand log_{7}(\sqrt[3]{x^5})

expand

\frac{5}{3} lo g_{7} (x)

Solution steps

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

Simplify

= lo g_{7} (x) + \frac{1}{3} lo g_{7} (x^{2})

\frac{1}{3} lo g_{7} (x^{2}) = \frac{2}{3} lo g_{7} (x)

= lo g_{7} (x) + \frac{2}{3} lo g_{7} (x)

Factor out common term

lo g_{7} (x)

= lo g_{7} (x) (1 + \frac{2}{3})

1 + \frac{2}{3} = \frac{5}{3}

= \frac{5}{3} lo g_{7} (x)

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What is expand log_{7}(\sqrt[3]{x^5}) ?
The solution to expand log_{7}(\sqrt[3]{x^5}) is 5/3 log_{7}(x)