What is log_{b}((xy^4)/(z^6)) ?

The solution to log_{b}((xy^4)/(z^6)) is log_{b}(x)+4log_{b}(y)-6log_{b}(z)

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simplify log_{b}((xy^4)/(z^6))

simplify

lo g_{b} (\frac{x y ^{4}}{z ^{6}})

lo g_{b} (x) + 4 lo g_{b} (y) - 6 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x y ^{4}}{z ^{6}})

Apply log rule:

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

lo g_{b} (\frac{x y ^{4}}{z ^{6}}) = lo g_{b} (x y^{4}) - lo g_{b} (z^{6})

= lo g_{b} (x y^{4}) - lo g_{b} (z^{6})

lo g_{b} (x y^{4}) = lo g_{b} (x) + 4 lo g_{b} (y)

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

= lo g_{b} (x) + 4 lo g_{b} (y) - 6 lo g_{b} (z)

\frac{1}{3} \cdot ln (64) - ln (12)

5 ln (x - 6) - ln (x^{2} - 11 x + 30) + 2 ln (x - 5)

5 ln (x + 1) + 6 ln (x)

\frac{1}{2} lo g_{10} (b) + 5 lo g_{10} (c)

ln (\frac{81162081}{390625})

What is log_{b}((xy^4)/(z^6)) ?
The solution to log_{b}((xy^4)/(z^6)) is log_{b}(x)+4log_{b}(y)-6log_{b}(z)