What is 2/5 log_{10}(x)-log_{10}(y) ?

The solution to 2/5 log_{10}(x)-log_{10}(y) is log_{10}((x^{2/5})/y)

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simplify 2/5 log_{10}(x)-log_{10}(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

\frac{2}{5} lo g_{10} (x) = lo g_{10} (x^{\frac{2}{5}})

= lo g_{10} (x^{\frac{2}{5}}) - lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x^{\frac{2}{5}}) - lo g_{10} (y) = lo g_{10} (\frac{x ^{\frac{2}{5}}}{y})

= lo g_{10} (\frac{x ^{\frac{2}{5}}}{y})

1 + ln (2 x)

ln (\frac{e ^{iπ}}{4 + 3 e ^{iπ}})

lo g_{8} (8 x)

lo g_{3} (4) + lo g_{3} (6)

lo g_{4} (\frac{1}{16} m n^{2})

What is 2/5 log_{10}(x)-log_{10}(y) ?
The solution to 2/5 log_{10}(x)-log_{10}(y) is log_{10}((x^{2/5})/y)