What is log_{3}(2x)-log_{3}(x-2) ?

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

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simplify log_{3}(2x)-log_{3}(x-2)

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

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