What is expand log_{5}((sqrt(5x^9))/y) ?

The solution to expand log_{5}((sqrt(5x^9))/y) is log_{5}(sqrt(5)sqrt(x)sqrt(x^8))-log_{5}(y)

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expand log_{5}((sqrt(5x^9))/y)

expand

lo g_{5} (\frac{5 x ^{9}}{y})

lo g_{5} (5 x x^{8}) - lo g_{5} (y)

Solution steps

lo g_{5} (\frac{5 x ^{9}}{y})

Apply log rule:

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

lo g_{5} (\frac{5 x ^{9}}{y}) = lo g_{5} (5 x^{9}) - lo g_{5} (y)

= lo g_{5} (5 x^{9}) - lo g_{5} (y)

5 x^{9} = 5 x x^{8}

= lo g_{5} (5 x x^{8}) - lo g_{5} (y)

lo g_{10} (3) + lo g_{10} (4) - lo g_{10} (2)

lo g_{a} (\frac{x ^{3} w}{y ^{2} z ^{4}})

- lo g_{10} (1.4 \cdot 1 0^{- 5})

\frac{1}{2} lo g_{10} (x) + 5 lo g_{10} (y)

(lo g_{b} (x) - lo g_{b} (y)) + 7 lo g_{b} (v)

What is expand log_{5}((sqrt(5x^9))/y) ?
The solution to expand log_{5}((sqrt(5x^9))/y) is log_{5}(sqrt(5)sqrt(x)sqrt(x^8))-log_{5}(y)