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

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

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

simplify

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

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

Solution steps

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

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

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

lo g_{12} (12 x)

lo g_{10} (\frac{x}{1000})

ln (\frac{z}{x y})

lo g_{10} (\frac{x}{y ^{3}})

\frac{1}{2} lo g_{10} (a) - 3 lo g_{10} (b)

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