What is 4log_{10}(x)-1/3 log_{10}(y) ?

The solution to 4log_{10}(x)-1/3 log_{10}(y) is log_{10}((x^4y^{2/3})/y)

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simplify 4log_{10}(x)-1/3 log_{10}(y)

simplify

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

lo g_{10} (\frac{x ^{4} y ^{\frac{2}{3}}}{y})

Solution steps

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

Apply log rule:

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

4 lo g_{10} (x) = lo g_{10} (x^{4})

= lo g_{10} (x^{4}) - \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^{4}) - 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^{4}) - lo g_{10} (y^{\frac{1}{3}}) = lo g_{10} (\frac{x ^{4}}{y ^{\frac{1}{3}}})

= lo g_{10} (\frac{x ^{4}}{y ^{\frac{1}{3}}})

Simplify

\frac{x ^{4}}{y ^{\frac{1}{3}}} : \frac{x ^{4} y ^{\frac{2}{3}}}{y}

= lo g_{10} (\frac{x ^{4} y ^{\frac{2}{3}}}{y})

lo g_{6} (x y)

ln (\frac{e ^{x} - 1}{e ^{x} + 1})

lo g_{10} (\frac{x ^{4} z ^{3}}{y})

- lo g_{10} (2 \cdot 1 0^{- 6})

ln (\frac{e ^{4}}{10})

What is 4log_{10}(x)-1/3 log_{10}(y) ?
The solution to 4log_{10}(x)-1/3 log_{10}(y) is log_{10}((x^4y^{2/3})/y)