What is log_{b}((x^2*y)/(z^6)) ?

The solution to log_{b}((x^2*y)/(z^6)) is 2log_{b}(x)+log_{b}(y)-6log_{b}(z)

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simplify log_{b}((x^2*y)/(z^6))

simplify

lo g_{b} (\frac{x ^{2} \cdot y}{z ^{6}})

2 lo g_{b} (x) + lo g_{b} (y) - 6 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x ^{2} y}{z ^{6}})

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 ^{6}}) = lo g_{b} (x^{2} y) - lo g_{b} (z^{6})

= lo g_{b} (x^{2} y) - lo g_{b} (z^{6})

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

lo g_{b} (z^{6}) = 6 lo g_{b} (z)

= 2 lo g_{b} (x) + lo g_{b} (y) - 6 lo g_{b} (z)

\frac{1}{2} lo g_{4} (25) + lo g_{4} (2)

- \frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1})

- \frac{6}{9} lo g_{2} (\frac{6}{9}) - \frac{3}{9} lo g_{2} (\frac{3}{9})

4 lo g_{b} (2) + lo g_{b} (5)

What is log_{b}((x^2*y)/(z^6)) ?
The solution to log_{b}((x^2*y)/(z^6)) is 2log_{b}(x)+log_{b}(y)-6log_{b}(z)