What is 2log_{6}(x)-3log_{6}(y) ?

The solution to 2log_{6}(x)-3log_{6}(y) is log_{6}((x^2)/(y^3))

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simplify 2log_{6}(x)-3log_{6}(y)

simplify

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

lo g_{6} (\frac{x ^{2}}{y ^{3}})

Solution steps

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

Apply log rule:

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

2 lo g_{6} (x) = lo g_{6} (x^{2})

= lo g_{6} (x^{2}) - 3 lo g_{6} (y)

Apply log rule:

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

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

= lo g_{6} (x^{2}) - lo g_{6} (y^{3})

Apply log rule:

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

lo g_{6} (x^{2}) - lo g_{6} (y^{3}) = lo g_{6} (\frac{x ^{2}}{y ^{3}})

= lo g_{6} (\frac{x ^{2}}{y ^{3}})

5 ln (x) + 6 ln (y)

lo g_{10} (\frac{7 x ( 2 - x )}{2 ( x - 1 ) ^{3}})

ln (\frac{1000000}{415382})

lo g_{10} (x) - 6 lo g_{10} (y) + 7 lo g_{10} (z)

ln (\frac{e ^{5}}{11})

What is 2log_{6}(x)-3log_{6}(y) ?
The solution to 2log_{6}(x)-3log_{6}(y) is log_{6}((x^2)/(y^3))