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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{2}{3 x ^{3} y})

2 ln (x) - \frac{1}{3} ln (x) + 3 ln (x - 1) + 3 ln (x^{2} - 2 x + 1)

lo g_{4} (\frac{y}{64})

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

ln (e) + ln (e) + ln (1) + ln (e^{l n (10)})

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