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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

- \frac{1}{2} - ln (\frac{1}{3})

ln (4 x^{2}) + ln (3 x^{2})

lo g_{10} (\frac{3 x}{4 y ^{2}})

lo g_{4} (3) + 5 lo g_{4} (y)

ln (\frac{x}{x + 3})

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