What is expand log_{3}((sqrt(3x^5))/y) ?

The solution to expand log_{3}((sqrt(3x^5))/y) is log_{3}(sqrt(3)sqrt(x)sqrt(x^4))-log_{3}(y)

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expand log_{3}((sqrt(3x^5))/y)

expand

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

lo g_{3} (3 x x^{4}) - lo g_{3} (y)

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

3 x^{5} = 3 x x^{4}

= lo g_{3} (3 x x^{4}) - lo g_{3} (y)

- ln (\frac{1}{4})

lo g_{10} (2 x^{4}) + lo g_{10} (3 x^{5})

ln (y) + ln (z)

lo g_{10} (\frac{y}{4 y + 8})

What is expand log_{3}((sqrt(3x^5))/y) ?
The solution to expand log_{3}((sqrt(3x^5))/y) is log_{3}(sqrt(3)sqrt(x)sqrt(x^4))-log_{3}(y)