What is log_{3}(2)+1/2 log_{3}(y) ?

The solution to log_{3}(2)+1/2 log_{3}(y) is log_{3}(2y^{1/2})

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simplify log_{3}(2)+1/2 log_{3}(y)

simplify

lo g_{3} (2) + \frac{1}{2} lo g_{3} (y)

lo g_{3} (2 y^{\frac{1}{2}})

Solution steps

lo g_{3} (2) + \frac{1}{2} lo g_{3} (y)

Apply log rule:

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

\frac{1}{2} lo g_{3} (y) = lo g_{3} (y^{\frac{1}{2}})

= lo g_{3} (2) + lo g_{3} (y^{\frac{1}{2}})

Apply log rule:

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

lo g_{3} (2) + lo g_{3} (y^{\frac{1}{2}}) = lo g_{3} (2 y^{\frac{1}{2}})

= lo g_{3} (2 y^{\frac{1}{2}})

\frac{1}{2} ln (3 c) + \frac{1}{2} ln (4) d - 2 ln (5 e)

- 5137.521 + 1239.973 ln (\frac{2018}{30})

ln (0.6889 \cdot π)

lo g_{16} (\frac{1}{18})

\frac{1}{5} ln (b^{2} + 3) - \frac{1}{5} ln (b + 3)

What is log_{3}(2)+1/2 log_{3}(y) ?
The solution to log_{3}(2)+1/2 log_{3}(y) is log_{3}(2y^{1/2})