What is log_{b}((x^2*y)/(z^9)) ?

The solution to log_{b}((x^2*y)/(z^9)) is 2log_{b}(x)+log_{b}(y)-9log_{b}(z)

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simplify log_{b}((x^2*y)/(z^9))

simplify

lo g_{b} (\frac{x ^{2} \cdot y}{z ^{9}})

2 lo g_{b} (x) + lo g_{b} (y) - 9 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{9}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{b} (\frac{x ^{2} y}{z ^{9}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{9})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{9})

lo g_{b} (x^{2} y) = 2 lo g_{b} (x) + lo g_{b} (y)

lo g_{b} (z^{9}) = 9 lo g_{b} (z)

= 2 lo g_{b} (x) + lo g_{b} (y) - 9 lo g_{b} (z)

ln (x e^{2 x})

4 lo g_{c} (x) - 6 lo g_{c} (y^{5})

ln (\frac{5}{x})

ln (10 e^{2})

What is log_{b}((x^2*y)/(z^9)) ?
The solution to log_{b}((x^2*y)/(z^9)) is 2log_{b}(x)+log_{b}(y)-9log_{b}(z)