What is log_{10}((x^5)/(z^3sqrt(y^2))) ?

The solution to log_{10}((x^5)/(z^3sqrt(y^2))) is 5log_{10}(x)-3log_{10}(z)-log_{10}(y)

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simplify log_{10}((x^5)/(z^3sqrt(y^2)))

simplify

lo g_{10} (\frac{x ^{5}}{z ^{3} y ^{2}})

5 lo g_{10} (x) - 3 lo g_{10} (z) - lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x ^{5}}{z ^{3} y ^{2}})

Simplify

\frac{x ^{5}}{z ^{3} y ^{2}} : \frac{x ^{5}}{z ^{3} y}

= lo g_{10} (\frac{x ^{5}}{z ^{3} y})

Apply log rule:

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

lo g_{10} (\frac{x ^{5}}{z ^{3} y}) = lo g_{10} (x^{5}) - lo g_{10} (z^{3} y)

= lo g_{10} (x^{5}) - lo g_{10} (z^{3} y)

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

lo g_{10} (z^{3} y) = 3 lo g_{10} (z) + lo g_{10} (y)

= 5 lo g_{10} (x) - (3 lo g_{10} (z) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{10} (z) + lo g_{10} (y)) = - 3 lo g_{10} (z) - lo g_{10} (y)

= 5 lo g_{10} (x) - 3 lo g_{10} (z) - lo g_{10} (y)

\frac{1}{4} lo g_{2} (4) + \frac{3}{4} lo g_{2} (\frac{4}{3})

lo g_{10} (8) - 2 lo g_{10} (2) + 4 lo g_{10} (x)

lo g_{2} (\frac{8}{x + 2})

\frac{1}{2} lo g_{3} (x) + 2 lo g_{3} (x - 2) - 5 lo g_{3} (2)

2 lo g_{6} (7) - 8 lo g_{6} (10)

What is log_{10}((x^5)/(z^3sqrt(y^2))) ?
The solution to log_{10}((x^5)/(z^3sqrt(y^2))) is 5log_{10}(x)-3log_{10}(z)-log_{10}(y)