What is log_{10}((x^2y^{18})/(z^8)) ?

The solution to log_{10}((x^2y^{18})/(z^8)) is 2log_{10}(x)+18log_{10}(y)-8log_{10}(z)

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simplify log_{10}((x^2y^{18})/(z^8))

simplify

lo g_{10} (\frac{x ^{2} y ^{18}}{z ^{8}})

2 lo g_{10} (x) + 18 lo g_{10} (y) - 8 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{2} y ^{18}}{z ^{8}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} y ^{18}}{z ^{8}}) = lo g_{10} (x^{2} y^{18}) - lo g_{10} (z^{8})

= lo g_{10} (x^{2} y^{18}) - lo g_{10} (z^{8})

lo g_{10} (x^{2} y^{18}) = 2 lo g_{10} (x) + 18 lo g_{10} (y)

lo g_{10} (z^{8}) = 8 lo g_{10} (z)

= 2 lo g_{10} (x) + 18 lo g_{10} (y) - 8 lo g_{10} (z)

ln (\frac{r}{2 s})

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lo g_{10} ((m^{n}) \cdot (p^{q}))

7 lo g_{2} (u) + 4 lo g_{2} (v)

ln (\frac{e ^{9}}{7})

What is log_{10}((x^2y^{18})/(z^8)) ?
The solution to log_{10}((x^2y^{18})/(z^8)) is 2log_{10}(x)+18log_{10}(y)-8log_{10}(z)