What is log_{a}(m^{1/4}n^{7/2}) ?

The solution to log_{a}(m^{1/4}n^{7/2}) is 1/4 log_{a}(m)+7/2 log_{a}(n)

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simplify log_{a}(m^{1/4}n^{7/2})

simplify

lo g_{a} (m^{\frac{1}{4}} n^{\frac{7}{2}})

\frac{1}{4} lo g_{a} (m) + \frac{7}{2} lo g_{a} (n)

Solution steps

lo g_{a} (m^{\frac{1}{4}} n^{\frac{7}{2}})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{a} (m^{\frac{1}{4}} n^{\frac{7}{2}}) = lo g_{a} (m^{\frac{1}{4}}) + lo g_{a} (n^{\frac{7}{2}})

= lo g_{a} (m^{\frac{1}{4}}) + lo g_{a} (n^{\frac{7}{2}})

lo g_{a} (m^{\frac{1}{4}}) = \frac{1}{4} lo g_{a} (m)

lo g_{a} (n^{\frac{7}{2}}) = \frac{7}{2} lo g_{a} (n)

= \frac{1}{4} lo g_{a} (m) + \frac{7}{2} lo g_{a} (n)

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What is log_{a}(m^{1/4}n^{7/2}) ?
The solution to log_{a}(m^{1/4}n^{7/2}) is 1/4 log_{a}(m)+7/2 log_{a}(n)