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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 5))

2 lo g_{x} (- 3 lo g_{y} (+ 4 lo g_{z} (x)))

lo g_{10} (\frac{y ^{5}}{z ^{2} x ^{3}})

4 ln (x) + 2 ln (y)

4 lo g_{b} (q) - lo g_{b} (r)

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