What is 1/5 (log_{3}(x)+log_{3}(x-2)) ?

The solution to 1/5 (log_{3}(x)+log_{3}(x-2)) is 1/5 log_{3}(x(x-2))

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simplify 1/5 (log_{3}(x)+log_{3}(x-2))

simplify

\frac{1}{5} (lo g_{3} (x) + lo g_{3} (x - 2))

\frac{1}{5} lo g_{3} (x (x - 2))

Solution steps

\frac{1}{5} (lo g_{3} (x) + lo g_{3} (x - 2))

Apply log rule:

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

lo g_{3} (x) + lo g_{3} (x - 2) = lo g_{3} (x (x - 2))

= \frac{1}{5} lo g_{3} (x (x - 2))

lo g_{10} (5) + lo g_{10} (3)

lo g_{b} (\frac{x ^{3} y}{z ^{8}})

ln (x) + ln (2)

lo g_{5} (10 x)

\frac{1}{3} lo g_{10} (x) + 3 lo g_{10} (x - 3)

What is 1/5 (log_{3}(x)+log_{3}(x-2)) ?
The solution to 1/5 (log_{3}(x)+log_{3}(x-2)) is 1/5 log_{3}(x(x-2))