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

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

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

simplify

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

3 lo g_{10} (x) - 2 lo g_{10} (z) - lo g_{10} (y)

Solution steps

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

Apply log rule:

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

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

= lo g_{10} (x^{3}) - lo g_{10} (z^{2} y)

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

lo g_{10} (z^{2} y) = 2 lo g_{10} (z) + lo g_{10} (y)

= 3 lo g_{10} (x) - (2 lo g_{10} (z) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{10} (z) + lo g_{10} (y)) = - 2 lo g_{10} (z) - lo g_{10} (y)

= 3 lo g_{10} (x) - 2 lo g_{10} (z) - lo g_{10} (y)

ln (\frac{0.85}{1.7})

3 lo g_{a} (7 x^{6}) - \frac{1}{8} lo g_{a} (5 x + 19)

lo g_{\frac{a}{b}} (\frac{b}{a})

ln (\frac{8}{13})

\frac{1}{2} lo g_{b} (x) + 4 lo g_{b} (y) - 3 lo g_{b} (x)

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