What is 1/2 log_{9}(x)+log_{9}(y) ?

The solution to 1/2 log_{9}(x)+log_{9}(y) is log_{9}(x^{1/2}y)

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simplify 1/2 log_{9}(x)+log_{9}(y)

simplify

\frac{1}{2} lo g_{9} (x) + lo g_{9} (y)

lo g_{9} (x^{\frac{1}{2}} y)

Solution steps

\frac{1}{2} lo g_{9} (x) + lo g_{9} (y)

Apply log rule:

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

\frac{1}{2} lo g_{9} (x) = lo g_{9} (x^{\frac{1}{2}})

= lo g_{9} (x^{\frac{1}{2}}) + lo g_{9} (y)

Apply log rule:

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

lo g_{9} (x^{\frac{1}{2}}) + lo g_{9} (y) = lo g_{9} (y x^{\frac{1}{2}})

= lo g_{9} (x^{\frac{1}{2}} y)

ln (\frac{98}{45})

2 ln (x) - \frac{1}{5} ln (y)

lo g_{7} (2 x)

lo g_{b} (x + 1) + lo g_{b} (3) - lo g_{b} (x + 2)

lo g_{4} (\frac{16}{x + 9})

What is 1/2 log_{9}(x)+log_{9}(y) ?
The solution to 1/2 log_{9}(x)+log_{9}(y) is log_{9}(x^{1/2}y)