What is log_{b}((xy^3)/(w^3z)) ?

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

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simplify log_{b}((xy^3)/(w^3z))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{b} (w^{3} z) = 3 lo g_{b} (w) + lo g_{b} (z)

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

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{b} (w) + lo g_{b} (z)) = - 3 lo g_{b} (w) - lo g_{b} (z)

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

\frac{1}{5} ln (\frac{5}{4})

- ln (\frac{5}{9})

ln (\frac{14}{5})

\frac{1}{5} lo g_{10} (5)

ln (\frac{53}{55})

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