What is log_{b}((x^2y)/(z^5)) ?

The solution to log_{b}((x^2y)/(z^5)) is 2log_{b}(x)+log_{b}(y)-5log_{b}(z)

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simplify log_{b}((x^2y)/(z^5))

simplify

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

2 lo g_{b} (x) + lo g_{b} (y) - 5 lo g_{b} (z)

Solution steps

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

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 ^{5}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{5})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{5})

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

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

= 2 lo g_{b} (x) + lo g_{b} (y) - 5 lo g_{b} (z)

lo g_{2} (3) + lo g_{2} (10)

9 ln (x) - 3 ln (y)

3 ln (x) - 5 ln (y)

lo g_{5} (1000) + lo g_{4 a} (64 a^{3})

What is log_{b}((x^2y)/(z^5)) ?
The solution to log_{b}((x^2y)/(z^5)) is 2log_{b}(x)+log_{b}(y)-5log_{b}(z)