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

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

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

simplify

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

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

Solution steps

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

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

- 2 ln (5 x)

2 lo g_{3} (5) - lo g_{3} (14) + lo g_{9} (3)

lo g_{10} (18) + lo g_{10} (8) - 2 lo g_{10} (25)

lo g_{10} (p) + 2 lo g_{10} (8 s)

ln (x (x - 1))

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