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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

ln (\frac{n}{n + 1})

lo g_{2} (21) - lo g_{2} (7)

ln (\frac{4 m ^{5}}{p})

\frac{3}{5} (- \frac{2}{3} lo g_{2} (\frac{2}{3}) - \frac{1}{3} lo g_{2} (\frac{1}{3}))

ln (\frac{9}{5})

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