What is 1/2 log_{4}(x)+1/2 log_{4}(y) ?

The solution to 1/2 log_{4}(x)+1/2 log_{4}(y) is log_{4}(x^{1/2}y^{1/2})

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simplify 1/2 log_{4}(x)+1/2 log_{4}(y)

simplify

\frac{1}{2} lo g_{4} (x) + \frac{1}{2} lo g_{4} (y)

lo g_{4} (x^{\frac{1}{2}} y^{\frac{1}{2}})

Solution steps

\frac{1}{2} lo g_{4} (x) + \frac{1}{2} lo g_{4} (y)

Apply log rule:

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

\frac{1}{2} lo g_{4} (x) = lo g_{4} (x^{\frac{1}{2}})

= lo g_{4} (x^{\frac{1}{2}}) + \frac{1}{2} lo g_{4} (y)

Apply log rule:

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

\frac{1}{2} lo g_{4} (y) = lo g_{4} (y^{\frac{1}{2}})

= lo g_{4} (x^{\frac{1}{2}}) + lo g_{4} (y^{\frac{1}{2}})

Apply log rule:

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

lo g_{4} (x^{\frac{1}{2}}) + lo g_{4} (y^{\frac{1}{2}}) = lo g_{4} (x^{\frac{1}{2}} y^{\frac{1}{2}})

= lo g_{4} (x^{\frac{1}{2}} y^{\frac{1}{2}})

lo g_{4} (7 e)

\frac{1}{2} ln (\frac{3}{2 e})

ln (\frac{23.3}{16.6})

4 lo g_{c} (8 y + 1) + \frac{1}{5} lo g_{c} (y + 6)

ln (\frac{( s + a )}{( s + b )})

What is 1/2 log_{4}(x)+1/2 log_{4}(y) ?
The solution to 1/2 log_{4}(x)+1/2 log_{4}(y) is log_{4}(x^{1/2}y^{1/2})