What is log_{2}(m)+1/2 log_{2}(n)+4 ?

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

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simplify log_{2}(m)+1/2 log_{2}(n)+4

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{2} (n) = lo g_{2} (n^{\frac{1}{2}})

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

Apply log rule:

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

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

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

lo g_{7} (6) - lo g_{7} (x)

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ln (\frac{( \frac{5.5}{12} )}{10})

2 ln (2) - \frac{1}{2} ln (x^{3} + 3 x)

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