What is log_{3}(x^{16}*\sqrt[3]{y^{14}}) ?

The solution to log_{3}(x^{16}*\sqrt[3]{y^{14}}) is 16log_{3}(x)+4log_{3}(y)+log_{3}(\sqrt[3]{y^2})

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simplify log_{3}(x^{16}*\sqrt[3]{y^{14}})

simplify

Solution steps

Simplify

Apply log rule:

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

lo g_{3} (x^{16}) = 16 lo g_{3} (x)

lo g_{3} (y^{4}) = 4 lo g_{3} (y)

ln (2) - ln (7)

lo g_{10} (\frac{( x ^{9} y ^{5} )}{( z ^{3} )})

ln (\frac{11782}{1000})

lo g_{3} (x yz)

- \frac{1}{2} lo g_{2} (3)

What is log_{3}(x^{16}*\sqrt[3]{y^{14}}) ?
The solution to log_{3}(x^{16}*\sqrt[3]{y^{14}}) is 16log_{3}(x)+4log_{3}(y)+log_{3}(\sqrt[3]{y^2})