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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (z^{5} y^{3}) : 5 lo g_{10} (z) + 3 lo g_{10} (y)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

2 lo g_{b} (x) + 4 lo g_{b} (z)

3 ln (x) - \frac{1}{2} ln (y) + 1

3 lo g_{4} (x) + 5 lo g_{4} (y) - 6 lo g_{4} (z)

lo g_{3} (z) + lo g_{3} (z + 5)

lo g_{10} (\frac{x}{10000 y ^{4}})

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