What is log_{9}(6x^3y^5z) ?

The solution to log_{9}(6x^3y^5z) is log_{9}(6)+3log_{9}(x)+5log_{9}(y)+log_{9}(z)

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simplify log_{9}(6x^3y^5z)

simplify

lo g_{9} (6 x^{3} y^{5} z)

lo g_{9} (6) + 3 lo g_{9} (x) + 5 lo g_{9} (y) + lo g_{9} (z)

Solution steps

lo g_{9} (6 x^{3} y^{5} z)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{9} (6 x^{3} y^{5} z) = lo g_{9} (6) + lo g_{9} (x^{3}) + lo g_{9} (y^{5}) + lo g_{9} (z)

= lo g_{9} (6) + lo g_{9} (x^{3}) + lo g_{9} (y^{5}) + lo g_{9} (z)

lo g_{9} (x^{3}) = 3 lo g_{9} (x)

lo g_{9} (y^{5}) = 5 lo g_{9} (y)

= lo g_{9} (6) + 3 lo g_{9} (x) + 5 lo g_{9} (y) + lo g_{9} (z)

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

lo g_{10} (\frac{7 x}{y ^{2}})

8 ln (x) - \frac{1}{6} ln (y)

lo g_{4} (\frac{x - 4}{y ^{2} ( 5 z )})

lo g_{7} (\frac{49 b ^{7} y ^{2} - 9}{y ( x + 9 ) ^{2}})

What is log_{9}(6x^3y^5z) ?
The solution to log_{9}(6x^3y^5z) is log_{9}(6)+3log_{9}(x)+5log_{9}(y)+log_{9}(z)