What is log_{b}(2/(z^5sqrt(y))) ?

The solution to log_{b}(2/(z^5sqrt(y))) is log_{b}(2)-5log_{b}(z)-log_{b}(sqrt(y))

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simplify log_{b}(2/(z^5sqrt(y)))

simplify

lo g_{b} (\frac{2}{z ^{5} y})

lo g_{b} (2) - 5 lo g_{b} (z) - lo g_{b} (y)

Solution steps

lo g_{b} (\frac{2}{z ^{5} y})

Apply log rule:

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

lo g_{b} (\frac{2}{z ^{5} y}) = lo g_{b} (2) - lo g_{b} (z^{5} y)

= lo g_{b} (2) - lo g_{b} (z^{5} y)

Simplify

lo g_{b} (z^{5} y) : 5 lo g_{b} (z) + lo g_{b} (y)

= lo g_{b} (2) - (5 lo g_{b} (z) + lo g_{b} (y))

Apply the distributive law:

- (a + b) = - a - b

- (5 lo g_{b} (z) + lo g_{b} (y)) = - 5 lo g_{b} (z) - lo g_{b} (y)

= lo g_{b} (2) - 5 lo g_{b} (z) - lo g_{b} (y)

lo g_{4} (64 x^{5})

ln (x) + 5 ln (y)

ln ((\frac{m ^{5}}{n ^{2}})^{3})

lo g_{8} (10) - 2 lo g_{8} (3)

What is log_{b}(2/(z^5sqrt(y))) ?
The solution to log_{b}(2/(z^5sqrt(y))) is log_{b}(2)-5log_{b}(z)-log_{b}(sqrt(y))