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

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

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

simplify

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

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

Solution steps

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

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

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

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

= 2 lo g_{b} (x) - (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)

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

4 lo g_{3} (x^{2}) - 3 lo g_{3} (x^{3})

lo g_{10} (6) - lo g_{10} (3) + 2 lo g_{10} (7)

lo g_{3} (\frac{9}{x - 1})

ln (\frac{e}{x})

lo g_{4} (5 x^{2})

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