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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

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

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

Simplify

\frac{x ^{2}}{y ^{\frac{1}{3}}} : \frac{x ^{2} y ^{\frac{2}{3}}}{y}

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

\frac{1}{3} ln (\frac{14}{7})

ln (5) - 2 ln (2)

- lo g_{10} (7.9 \cdot 1 0^{- 13})

1.41 - \frac{0.0591}{6} \cdot lo g_{10} (\frac{0.001}{0.5})

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