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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5 ln (cos^{2} (t)) + 5 ln (1 + tan^{2} (t))

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

- lo g_{10} (2.5 \cdot 1 0^{- 7})

lo g_{10} (\frac{x z ^{2}}{y})

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

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