What is log_{b}((x^3*y)/(z^2)) ?

The solution to log_{b}((x^3*y)/(z^2)) is 3log_{b}(x)+log_{b}(y)-2log_{b}(z)

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simplify log_{b}((x^3*y)/(z^2))

simplify

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

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

Solution steps

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

Apply log rule:

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

lo g_{b} (\frac{x ^{3} y}{z ^{2}}) = lo g_{b} (x^{3} y) - lo g_{b} (z^{2})

= lo g_{b} (x^{3} y) - lo g_{b} (z^{2})

lo g_{b} (x^{3} y) = 3 lo g_{b} (x) + lo g_{b} (y)

lo g_{b} (z^{2}) = 2 lo g_{b} (z)

= 3 lo g_{b} (x) + lo g_{b} (y) - 2 lo g_{b} (z)

4 lo g_{b} (y) + 7 lo g_{b} (z)

lo g_{7} (\frac{w ^{2}}{v})

lo g_{2} (3 x y)

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

What is log_{b}((x^3*y)/(z^2)) ?
The solution to log_{b}((x^3*y)/(z^2)) is 3log_{b}(x)+log_{b}(y)-2log_{b}(z)