What is 3log_{6}(x)-log_{6}(y) ?

The solution to 3log_{6}(x)-log_{6}(y) is log_{6}((x^3)/y)

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simplify 3log_{6}(x)-log_{6}(y)

simplify

3 lo g_{6} (x) - lo g_{6} (y)

lo g_{6} (\frac{x ^{3}}{y})

Solution steps

3 lo g_{6} (x) - lo g_{6} (y)

Apply log rule:

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

3 lo g_{6} (x) = lo g_{6} (x^{3})

= lo g_{6} (x^{3}) - lo g_{6} (y)

Apply log rule:

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

lo g_{6} (x^{3}) - lo g_{6} (y) = lo g_{6} (\frac{x ^{3}}{y})

= lo g_{6} (\frac{x ^{3}}{y})

ln (\frac{y}{x}) - \frac{y}{x}

- 2 lo g_{e} (\frac{3}{2})

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

ln (\frac{1}{1 - 20})

ln (x^{2} x - 1)

What is 3log_{6}(x)-log_{6}(y) ?
The solution to 3log_{6}(x)-log_{6}(y) is log_{6}((x^3)/y)