What is 2/3 log_{10}(x)-1/3 log_{10}(y) ?

The solution to 2/3 log_{10}(x)-1/3 log_{10}(y) is log_{10}(\sqrt[3]{(x^2)/y})

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simplify 2/3 log_{10}(x)-1/3 log_{10}(y)

simplify

\frac{2}{3} lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

Solution steps

\frac{2}{3} lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{2}{3} lo g_{10} (x) = lo g_{10} (x^{\frac{2}{3}})

= lo g_{10} (x^{\frac{2}{3}}) - \frac{1}{3} lo g_{10} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{3} lo g_{10} (y) = lo g_{10} (y^{\frac{1}{3}})

= lo g_{10} (x^{\frac{2}{3}}) - lo g_{10} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{10} (x^{\frac{2}{3}}) - lo g_{10} (y^{\frac{1}{3}}) = lo g_{10} (\frac{x ^{\frac{2}{3}}}{y ^{\frac{1}{3}}})

= lo g_{10} (\frac{x ^{\frac{2}{3}}}{y ^{\frac{1}{3}}})

Combine same powers :

ln (\frac{1 - ( - 1 )}{1 + 2})

- lo g_{10} (5.08 \cdot 1 0^{- 5})

2.45 + lo g_{10} (\frac{0.047}{0.054})

ln (x) + \frac{2}{5} ln (5 u^{2} + 1)

- 9 ln (9 x) - (\frac{1}{9}) ln (2700 - 9 x)

What is 2/3 log_{10}(x)-1/3 log_{10}(y) ?
The solution to 2/3 log_{10}(x)-1/3 log_{10}(y) is log_{10}(\sqrt[3]{(x^2)/y})