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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

0.3 ln (\frac{10 + 104}{2})

ln (\frac{2 x ^{4}}{y ^{7}})

ln (\frac{0.525}{0.412})

- lo g_{10} (2.17 \cdot 1 0^{- 9})

ln (7) - ln (14) + ln (10)

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