What is 3(log_{6}(x)+2log_{6}(y)-4log_{6}(z)) ?

The solution to 3(log_{6}(x)+2log_{6}(y)-4log_{6}(z)) is 3log_{6}((xy^2)/(z^4))

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simplify 3(log_{6}(x)+2log_{6}(y)-4log_{6}(z))

simplify

3 (lo g_{6} (x) + 2 lo g_{6} (y) - 4 lo g_{6} (z))

3 lo g_{6} (\frac{x y ^{2}}{z ^{4}})

Solution steps

3 (lo g_{6} (x) + 2 lo g_{6} (y) - 4 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})

= 3 (lo g_{6} (x) + lo g_{6} (y^{2}) - 4 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})

= 3 (lo g_{6} (x y^{2}) - 4 lo g_{6} (z))

Apply log rule:

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

4 lo g_{6} (z) = lo g_{6} (z^{4})

= 3 (- lo g_{6} (z^{4}) + 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^{4}) = lo g_{6} (\frac{x y ^{2}}{z ^{4}})

= 3 lo g_{6} (\frac{x y ^{2}}{z ^{4}})

lo g_{b} (\frac{2.079}{1.946})

ln (17 x) - ln (17)

3 lo g_{10} (2 x) + 2 lo g_{10} (x)

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

lo g_{4} (x) - 3 lo g_{4} (y)

What is 3(log_{6}(x)+2log_{6}(y)-4log_{6}(z)) ?
The solution to 3(log_{6}(x)+2log_{6}(y)-4log_{6}(z)) is 3log_{6}((xy^2)/(z^4))