What is expand log_{3}(\sqrt[4]{m^5n^2}) ?

The solution to expand log_{3}(\sqrt[4]{m^5n^2}) is 5/4 log_{3}(m)+0.5log_{3}(n)

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expand log_{3}(\sqrt[4]{m^5n^2})

expand

\frac{5}{4} lo g_{3} (m) + 0.5 lo g_{3} (n)

Solution steps

Apply log rule:

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

Simplify

= lo g_{3} (m n) + \frac{1}{4} lo g_{3} (m)

lo g_{3} (m n) = lo g_{3} (m) + 0.5 lo g_{3} (n)

= lo g_{3} (m) + 0.5 lo g_{3} (n) + \frac{1}{4} lo g_{3} (m)

Group like terms

= \frac{1}{4} lo g_{3} (m) + lo g_{3} (m) + 0.5 lo g_{3} (n)

Add similar elements:

\frac{1}{4} lo g_{3} (m) + lo g_{3} (m) = \frac{5}{4} lo g_{3} (m)

= \frac{5}{4} lo g_{3} (m) + 0.5 lo g_{3} (n)

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What is expand log_{3}(\sqrt[4]{m^5n^2}) ?
The solution to expand log_{3}(\sqrt[4]{m^5n^2}) is 5/4 log_{3}(m)+0.5log_{3}(n)