What is 3(log_{6}(x)+3log_{6}(y)-5log_{6}(z)) ?

The solution to 3(log_{6}(x)+3log_{6}(y)-5log_{6}(z)) is 3log_{6}((xy^3)/(z^5))

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simplify 3(log_{6}(x)+3log_{6}(y)-5log_{6}(z))

simplify

3 (lo g_{6} (x) + 3 lo g_{6} (y) - 5 lo g_{6} (z))

3 lo g_{6} (\frac{x y ^{3}}{z ^{5}})

Solution steps

3 (lo g_{6} (x) + 3 lo g_{6} (y) - 5 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}) - 5 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}) - 5 lo g_{6} (z))

Apply log rule:

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

5 lo g_{6} (z) = lo g_{6} (z^{5})

= 3 (- lo g_{6} (z^{5}) + 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^{5}) = lo g_{6} (\frac{x y ^{3}}{z ^{5}})

= 3 lo g_{6} (\frac{x y ^{3}}{z ^{5}})

ln (9) - ln (4)

lo g_{2} (8 x) \frac{1}{3}

ln (\frac{2}{9})

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

lo g_{10} (x y^{2})

What is 3(log_{6}(x)+3log_{6}(y)-5log_{6}(z)) ?
The solution to 3(log_{6}(x)+3log_{6}(y)-5log_{6}(z)) is 3log_{6}((xy^3)/(z^5))