What is 1/2 (log_{6}(x)+log_{6}(y)) ?

The solution to 1/2 (log_{6}(x)+log_{6}(y)) is 1/2 log_{6}(xy)

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simplify 1/2 (log_{6}(x)+log_{6}(y))

simplify

\frac{1}{2} (lo g_{6} (x) + lo g_{6} (y))

\frac{1}{2} lo g_{6} (x y)

Solution steps

\frac{1}{2} (lo g_{6} (x) + lo g_{6} (y))

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{6} (x) + lo g_{6} (y) = lo g_{6} (x y)

= \frac{1}{2} lo g_{6} (x y)

- lo g_{10} (3.3 \cdot 1 0^{- 6})

2 lo g_{a} (3) - 2 lo g_{a} (2)

ln (2) - ln (x)

\frac{1}{4} ln (x) + 5 [ln (x - 2) - \frac{3}{10} ln (x + 2)]

8 ln (x) - \frac{1}{9} ln (y)

What is 1/2 (log_{6}(x)+log_{6}(y)) ?
The solution to 1/2 (log_{6}(x)+log_{6}(y)) is 1/2 log_{6}(xy)