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

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

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

simplify

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

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

Solution steps

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

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

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

Simplify

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

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

ln (1 e^{- 0.00018})

4 lo g_{\frac{5}{3}} (2)

- ln (7 - 3) + 2 ln (7 - 2)

10 (lo g_{10} (x) - lo g_{10} (0.0625))

lo g_{5} (- 3 x)

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