What is log_{3}(sqrt(x))-log_{3}(x^8) ?

The solution to log_{3}(sqrt(x))-log_{3}(x^8) is log_{3}((sqrt(x))/(x^8))

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simplify log_{3}(sqrt(x))-log_{3}(x^8)

simplify

lo g_{3} (x) - lo g_{3} (x^{8})

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

Solution steps

lo g_{3} (x) - lo g_{3} (x^{8})

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^{8}) = lo g_{3} (\frac{x}{x ^{8}})

= lo g_{3} (\frac{x}{x ^{8}})

6 lo g_{8} (11) - 30 lo g_{8} (3)

lo g_{a} (x^{2}) + 3 lo g_{a} (x) - 2 lo g_{a} (4 x)

3 ln (3) + 3 ln (y)

lo g_{b} (y^{5} z)

What is log_{3}(sqrt(x))-log_{3}(x^8) ?
The solution to log_{3}(sqrt(x))-log_{3}(x^8) is log_{3}((sqrt(x))/(x^8))