What is log_{3}(sqrt(x))-log_{3}(x^5) ?

The solution to log_{3}(sqrt(x))-log_{3}(x^5) is log_{3}((sqrt(x))/(x^5))

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simplify log_{3}(sqrt(x))-log_{3}(x^5)

simplify

lo g_{3} (x) - lo g_{3} (x^{5})

lo g_{3} (\frac{x}{x ^{5}})

Solution steps

lo g_{3} (x) - lo g_{3} (x^{5})

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^{5}) = lo g_{3} (\frac{x}{x ^{5}})

= lo g_{3} (\frac{x}{x ^{5}})

lo g_{10} (\frac{x}{10000})

- \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣ + C

lo g_{5} (\frac{125}{x - 1})

ln (x (x - 3))

- lo g_{10} (7.7 \cdot 1 0^{- 3})

What is log_{3}(sqrt(x))-log_{3}(x^5) ?
The solution to log_{3}(sqrt(x))-log_{3}(x^5) is log_{3}((sqrt(x))/(x^5))