What is expand log_{3}((sqrt(3x^7))/y) ?

The solution to expand log_{3}((sqrt(3x^7))/y) is log_{3}(sqrt(3)sqrt(x)sqrt(x^6))-log_{3}(y)

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expand log_{3}((sqrt(3x^7))/y)

expand

lo g_{3} (\frac{3 x ^{7}}{y})

lo g_{3} (3 x x^{6}) - lo g_{3} (y)

Solution steps

lo g_{3} (\frac{3 x ^{7}}{y})

Apply log rule:

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

lo g_{3} (\frac{3 x ^{7}}{y}) = lo g_{3} (3 x^{7}) - lo g_{3} (y)

= lo g_{3} (3 x^{7}) - lo g_{3} (y)

3 x^{7} = 3 x x^{6}

= lo g_{3} (3 x x^{6}) - lo g_{3} (y)

lo g_{10} (83 x y)

lo g_{10} (x^{2} + 9 x + 8) - lo g_{10} (x^{2} - 64)

lo g_{b} (x^{3} y^{2} z)

lo g_{10} (\frac{6 ( 5 + x ) ^{4}}{x ^{2}})

2 ln (3) + ln (2)

What is expand log_{3}((sqrt(3x^7))/y) ?
The solution to expand log_{3}((sqrt(3x^7))/y) is log_{3}(sqrt(3)sqrt(x)sqrt(x^6))-log_{3}(y)