What is expand log_{5}((sqrt(5x^7))/y) ?

The solution to expand log_{5}((sqrt(5x^7))/y) is log_{5}(sqrt(5)sqrt(x)sqrt(x^6))-log_{5}(y)

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expand log_{5}((sqrt(5x^7))/y)

expand

lo g_{5} (\frac{5 x ^{7}}{y})

lo g_{5} (5 x x^{6}) - lo g_{5} (y)

Solution steps

lo g_{5} (\frac{5 x ^{7}}{y})

Apply log rule:

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

lo g_{5} (\frac{5 x ^{7}}{y}) = lo g_{5} (5 x^{7}) - lo g_{5} (y)

= lo g_{5} (5 x^{7}) - lo g_{5} (y)

5 x^{7} = 5 x x^{6}

= lo g_{5} (5 x x^{6}) - lo g_{5} (y)

[ln (x^{5} - 1) - ln (x^{3} - 1)]

- (\frac{4}{6}) lo g_{2} (\frac{4}{6}) - (\frac{2}{6}) lo g_{2} (\frac{2}{6})

ln (\frac{5}{1})

ln (x e^{- x y})

lo g_{18} (\frac{13 r}{s})

What is expand log_{5}((sqrt(5x^7))/y) ?
The solution to expand log_{5}((sqrt(5x^7))/y) is log_{5}(sqrt(5)sqrt(x)sqrt(x^6))-log_{5}(y)