What is log_{b}((x^3y)/(z^4)) ?

The solution to log_{b}((x^3y)/(z^4)) is 3log_{b}(x)+log_{b}(y)-4log_{b}(z)

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simplify log_{b}((x^3y)/(z^4))

simplify

lo g_{b} (\frac{x ^{3} y}{z ^{4}})

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

Solution steps

lo g_{b} (\frac{x ^{3} 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 ^{3} y}{z ^{4}}) = lo g_{b} (x^{3} y) - lo g_{b} (z^{4})

= lo g_{b} (x^{3} y) - lo g_{b} (z^{4})

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

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

= 3 lo g_{b} (x) + lo g_{b} (y) - 4 lo g_{b} (z)

lo g_{5} (\frac{625}{y})

ln (\frac{x}{y}) - 2 ln (x^{3}) - 4 ln (y)

ln (\frac{e ^{x l n (3)}}{3})

What is log_{b}((x^3y)/(z^4)) ?
The solution to log_{b}((x^3y)/(z^4)) is 3log_{b}(x)+log_{b}(y)-4log_{b}(z)