What is log_{b}((x^2*y)/(z^4)) ?

The solution to log_{b}((x^2*y)/(z^4)) is 2log_{b}(x)+log_{b}(y)-4log_{b}(z)

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simplify log_{b}((x^2*y)/(z^4))

simplify

lo g_{b} (\frac{x ^{2} \cdot y}{z ^{4}})

2 lo g_{b} (x) + lo g_{b} (y) - 4 lo g_{b} (z)

Solution steps

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

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 ^{4}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{4})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{4})

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

lo g_{b} (z^{4}) = 4 lo g_{b} (z)

= 2 lo g_{b} (x) + lo g_{b} (y) - 4 lo g_{b} (z)

lo g_{10} (3) - lo g_{10} (6) - lo g_{10} (5)

9 ln (x) - \frac{1}{3} ln (y)

lo g_{b} (\frac{p ^{4} q ^{6}}{m ^{4} b ^{9}})

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

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 8

What is log_{b}((x^2*y)/(z^4)) ?
The solution to log_{b}((x^2*y)/(z^4)) is 2log_{b}(x)+log_{b}(y)-4log_{b}(z)