What is expand log_{6}(sqrt(3mn^8)) ?

The solution to expand log_{6}(sqrt(3mn^8)) is 4log_{6}(n)+1/2 log_{6}(m)+1/2 log_{6}(3)

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expand log_{6}(sqrt(3mn^8))

expand

lo g_{6} (3 m n^{8})

4 lo g_{6} (n) + \frac{1}{2} lo g_{6} (m) + \frac{1}{2} lo g_{6} (3)

Solution steps

lo g_{6} (3 m n^{8})

3 m n^{8} = 3 n^{4} m

= lo g_{6} (3 n^{4} m)

Apply log rule:

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

lo g_{6} (3 n^{4} m) = lo g_{6} (n^{4} m) + lo g_{6} (3)

= lo g_{6} (n^{4} m) + lo g_{6} (3)

Simplify

lo g_{6} (3) : \frac{1}{2} lo g_{6} (3)

= lo g_{6} (n^{4} m) + \frac{1}{2} lo g_{6} (3)

lo g_{6} (n^{4} m) = 4 lo g_{6} (n) + \frac{1}{2} lo g_{6} (m)

= 4 lo g_{6} (n) + \frac{1}{2} lo g_{6} (m) + \frac{1}{2} lo g_{6} (3)

- \frac{8 x}{( x ^{2} - 4 ) ^{2}}

(3 - i)^{4}

(1 - 2 i)^{5}

(\frac{4}{16} x + \frac{5}{16} y + \frac{3}{16} z + \frac{4}{16} u)^{4}

\frac{- x ^{2} + y ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

What is expand log_{6}(sqrt(3mn^8)) ?
The solution to expand log_{6}(sqrt(3mn^8)) is 4log_{6}(n)+1/2 log_{6}(m)+1/2 log_{6}(3)